Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
86701	Find the Tangent Line at (3,2)	y = square root of x+1 ; (3,2)	$y = \sqrt{x + 1}$ $y = \sqrt{x + 1}$ ; $(3, 2)$ $(3, 2)$
86702	Find the Tangent Line at (-2,-8)	f(x)=x^3 , (-2,-8)	$f (x) = x^{3}$ $f (x) = x^{3}$ , $(- 2, - 8)$ $(- 2, - 8)$
86703	Find the Tangent Line at (1/6,6e)	y=(e^(6x))/x , (1/6,6e)	$y = \frac{e^{6 x}}{x}$ $y = \frac{e^{6 x}}{x}$ , $(\frac{1}{6}, 6 e)$ $(\frac{1}{6}, 6 e)$
86704	Find the Tangent Line at (π/2,3π)	y=6xsin(x) , (pi/2,3pi)	$y = 6 x \sin (x)$ $y = 6 x \sin (x)$ , $(\frac{π}{2}, 3 π)$ $(\frac{π}{2}, 3 π)$
86705	Find the Tangent Line at (0,7)	y=14/(1+e^(-x)) , (0,7)	$y = \frac{14}{(1 + e^{- x})}$ $y = \frac{14}{(1 + e^{- x})}$ , $(0, 7)$ $(0, 7)$
86706	Find the Tangent Line at (6,19)	y=2x^2-9x+1 , (6,19)	$y = 2 x^{2} - 9 x + 1$ $y = 2 x^{2} - 9 x + 1$ , $(6, 19)$ $(6, 19)$
86707	Find the Tangent Line at (-1,8)	f(x)=3-5x , (-1,8)	$f (x) = 3 - 5 x$ $f (x) = 3 - 5 x$ , $(- 1, 8)$ $(- 1, 8)$
86708	Find the Tangent Line at (-1,-4)	y=(8x)/(x^2+1) , (-1,-4)	$y = \frac{8 x}{x^{2} + 1}$ $y = \frac{8 x}{x^{2} + 1}$ , $(- 1, - 4)$ $(- 1, - 4)$
86709	Find the Tangent Line at (4,6)	f(x)=3 square root of x at (4,6)	$f (x) = 3 \sqrt{x}$ $f (x) = 3 \sqrt{x}$ at $(4, 6)$ $(4, 6)$
86710	Find the Tangent Line at (2,19)	y=2x^3-x^2+7 , (2,19)	$y = 2 x^{3} - x^{2} + 7$ $y = 2 x^{3} - x^{2} + 7$ , $(2, 19)$ $(2, 19)$
86711	Find the Tangent Line at x=1	y=x^(cot(x)) , x=1	$y = x^{\cot (x)}$ $y = x^{\cot (x)}$ , $x = 1$ $x = 1$
86712	Find the Tangent Line at (3,-6)	f(x)=x-x^2 at (3,-6)	$f (x) = x - x^{2}$ $f (x) = x - x^{2}$ at $(3, - 6)$ $(3, - 6)$
86713	Find the Tangent Line at (9,1/3)	f(x)=3/x at (9,1/3)	$f (x) = \frac{3}{x}$ $f (x) = \frac{3}{x}$ at $(9, \frac{1}{3})$ $(9, \frac{1}{3})$
86714	Find the Tangent Line at (1,3)	y=2x^3-x^2+2 , (1,3)	$y = 2 x^{3} - x^{2} + 2$ $y = 2 x^{3} - x^{2} + 2$ , $(1, 3)$ $(1, 3)$
86715	Find the Tangent Line at x=1/2⋅ln(5)	y=e^(2x) at x=1/2 natural log of 5	$y = e^{2 x}$ $y = e^{2 x}$ at $x = \frac{1}{2} \ln (5)$ $x = \frac{1}{2} \ln (5)$
86716	Find the Tangent Line at x=1	f(x)=1/x ; x=1	$f (x) = \frac{1}{x}$ $f (x) = \frac{1}{x}$ ; $x = 1$ $x = 1$
86717	Find the Tangent Line at x=11	f(x)=( natural log of x)^3 at x=11	$f (x) = \ln^{3} (x)$ $f (x) = \ln^{3} (x)$ at $x = 11$ $x = 11$
86718	Find the Tangent Line at (1,-8)	y=x^3-9x , (1,-8)	$y = x^{3} - 9 x$ $y = x^{3} - 9 x$ , $(1, - 8)$ $(1, - 8)$
86719	Find the Tangent Line at (1,1)	f(x)=1/(x^2) , (1,1)	$f (x) = \frac{1}{x^{2}}$ $f (x) = \frac{1}{x^{2}}$ , $(1, 1)$ $(1, 1)$
86720	Find the Tangent Line at (1,4)	y=3x^3-x^2+2 , (1,4)	$y = 3 x^{3} - x^{2} + 2$ $y = 3 x^{3} - x^{2} + 2$ , $(1, 4)$ $(1, 4)$
86721	Find the Tangent Line at (1,1)	x^2+xy+y^2=3 , (1,1)	$x^{2} + x y + y^{2} = 3$ $x^{2} + x y + y^{2} = 3$ , $(1, 1)$ $(1, 1)$
86722	Find the Tangent Line at (5,6)	f(x) = square root of 5x+11 , (5,6)	$f (x) = \sqrt{5 x + 11}$ $f (x) = \sqrt{5 x + 11}$ , $(5, 6)$ $(5, 6)$
86723	Find the Tangent Line at x=1	y=x^2 at x=1	$y = x^{2}$ $y = x^{2}$ at $x = 1$ $x = 1$
86724	Find the Tangent Line at (1,1/4)	y=(x^2)/(3+x) , (1,1/4)	$y = \frac{x^{2}}{3 + x}$ $y = \frac{x^{2}}{3 + x}$ , $(1, \frac{1}{4})$ $(1, \frac{1}{4})$
86725	Find the Tangent Line at (-1,1)	y=(-2x)/(x^2+1) at the origin and at the point (-1,1)	$y = \frac{- 2 x}{x^{2} + 1}$ $y = \frac{- 2 x}{x^{2} + 1}$ at the origin and at the point $(- 1, 1)$ $(- 1, 1)$
86726	Find the Tangent Line at (2,0)	y = natural log of x^2-3 , (2,0)	$y = \ln (x^{2} - 3)$ $y = \ln (x^{2} - 3)$ , $(2, 0)$ $(2, 0)$
86727	Find the Tangent Line at (0,2)	y=x^4+2e^x , (0,2)	$y = x^{4} + 2 e^{x}$ $y = x^{4} + 2 e^{x}$ , $(0, 2)$ $(0, 2)$
86728	Find the Tangent Line at (0,0)	f(x)=2xe^x , (0,0)	$f (x) = 2 x e^{x}$ $f (x) = 2 x e^{x}$ , $(0, 0)$ $(0, 0)$
86729	Find the Tangent Line at (-2,6)	f(x)=x^2+2 at (-2,6)	$f (x) = x^{2} + 2$ $f (x) = x^{2} + 2$ at $(- 2, 6)$ $(- 2, 6)$
86730	Find the Tangent Line at (16,8)	y=2 square root of x , (16,8)	$y = 2 \sqrt{x}$ $y = 2 \sqrt{x}$ , $(16, 8)$ $(16, 8)$
86731	Find the Tangent Line at (-1,1)	f(x)=x^4 , (-1,1)	$f (x) = x^{4}$ $f (x) = x^{4}$ , $(- 1, 1)$ $(- 1, 1)$
86732	Find the Tangent Line at (4,-1)	f(x)=1/(x-5) ; (4,-1)	$f (x) = \frac{1}{x - 5}$ $f (x) = \frac{1}{x - 5}$ ; $(4, - 1)$ $(4, - 1)$
86733	Find the Tangent Line at x=1	f(x)=5/(x^2) ; x=1	$f (x) = \frac{5}{x^{2}}$ $f (x) = \frac{5}{x^{2}}$ ; $x = 1$ $x = 1$
86734	Find the Tangent Line at (4,-2√(3))	x^2y^2-9x^2-4y^2=0 , (4,-2 square root of 3)	$x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0$ $x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0$ , $(4, - 2 \sqrt{3})$ $(4, - 2 \sqrt{3})$
86735	Find the Tangent Line at (-2,3)	y=x^2+x+1 at (-2,3)	$y = x^{2} + x + 1$ $y = x^{2} + x + 1$ at $(- 2, 3)$ $(- 2, 3)$
86736	Find the Tangent Line at (3,3)	g(x)=(7x)/(x+4) at (3,3)	$g (x) = \frac{7 x}{x + 4}$ $g (x) = \frac{7 x}{x + 4}$ at $(3, 3)$ $(3, 3)$
86737	Find the Tangent Line at (-4,-20)	y=x-x^2 , (-4,-20)	$y = x - x^{2}$ $y = x - x^{2}$ , $(- 4, - 20)$ $(- 4, - 20)$
86738	Find the Tangent Line at (2,6)	y^2-x^2y-6x=0 , (2,6)	$y^{2} - x^{2} y - 6 x = 0$ $y^{2} - x^{2} y - 6 x = 0$ , $(2, 6)$ $(2, 6)$
86739	Find the Tangent Line at (8,1/4)	f(x)=2/x at (8,1/4)	$f (x) = \frac{2}{x}$ $f (x) = \frac{2}{x}$ at $(8, \frac{1}{4})$ $(8, \frac{1}{4})$
86740	Find the Tangent Line at (0,0)	y=sin(7x)+sin(7x)^2 , (0,0)	$y = \sin (7 x) + \sin^{2} (7 x)$ $y = \sin (7 x) + \sin^{2} (7 x)$ , $(0, 0)$ $(0, 0)$
86741	Find the Tangent Line at (-2,16)	f(x)=x^4 , (-2,16)	$f (x) = x^{4}$ $f (x) = x^{4}$ , $(- 2, 16)$ $(- 2, 16)$
86742	Find the Tangent Line at x=9	f(x)=( natural log of x)^4 at x=9	$f (x) = \ln^{4} (x)$ $f (x) = \ln^{4} (x)$ at $x = 9$ $x = 9$
86743	Find the Tangent Line at (9,3)	x^2=y^4 , (9,3)	$x^{2} = y^{4}$ $x^{2} = y^{4}$ , $(9, 3)$ $(9, 3)$
86744	Find the Tangent Line at (π/4,-√(2)/2)	y=cos(3x) , (pi/4,-( square root of 2)/2)	$y = \cos (3 x)$ $y = \cos (3 x)$ , $(\frac{π}{4}, - \frac{\sqrt{2}}{2})$ $(\frac{π}{4}, - \frac{\sqrt{2}}{2})$
86745	Find the Tangent Line at (3,4)	x^2+y^2=25 , (3,4)	$x^{2} + y^{2} = 25$ $x^{2} + y^{2} = 25$ , $(3, 4)$ $(3, 4)$
86746	Find the Tangent Line at (6,19)	y=2x^2-9x+1 , (6,19)	$y = 2 x^{2} - 9 x + 1$ $y = 2 x^{2} - 9 x + 1$ , $(6, 19)$ $(6, 19)$
86747	Find the Tangent Line at x=1/3⋅ln(3)	y=e^(3x) at x=1/3 natural log of 3	$y = e^{3 x}$ $y = e^{3 x}$ at $x = \frac{1}{3} \ln (3)$ $x = \frac{1}{3} \ln (3)$
86748	Find the Tangent Line at (9,4)	square root of x+ square root of y=5 , (9,4)	$\sqrt{x} + \sqrt{y} = 5$ $\sqrt{x} + \sqrt{y} = 5$ , $(9, 4)$ $(9, 4)$
86749	Find the Tangent Line at (1,1/9)	y=(x^2)/(8+x) , (1,1/9)	$y = \frac{x^{2}}{8 + x}$ $y = \frac{x^{2}}{8 + x}$ , $(1, \frac{1}{9})$ $(1, \frac{1}{9})$
86750	Find the Tangent Line at x=1	f(x)=2x^3+3x-3 at x=1	$f (x) = 2 x^{3} + 3 x - 3$ $f (x) = 2 x^{3} + 3 x - 3$ at $x = 1$ $x = 1$
86751	Find the Tangent Line at (4,-1)	f(x)=1/(x-5) , (4,-1)	$f (x) = \frac{1}{x - 5}$ $f (x) = \frac{1}{x - 5}$ , $(4, - 1)$ $(4, - 1)$
86752	Find the Tangent Line at x=1/3⋅ln(2)	y=e^(3x) at x=1/3 natural log of 2	$y = e^{3 x}$ $y = e^{3 x}$ at $x = \frac{1}{3} \ln (2)$ $x = \frac{1}{3} \ln (2)$
86753	Find the Tangent Line at (1,-4)	y=x^3-3x^2-2 ; (1,-4)	$y = x^{3} - 3 x^{2} - 2$ $y = x^{3} - 3 x^{2} - 2$ ; $(1, - 4)$ $(1, - 4)$
86754	Find the Tangent Line at (8,4)	f(x) = square root of x+8 , (8,4)	$f (x) = \sqrt{x + 8}$ $f (x) = \sqrt{x + 8}$ , $(8, 4)$ $(8, 4)$
86755	Find the Tangent Line at (-2,5)	f(x)=x^2+1 at (-2,5)	$f (x) = x^{2} + 1$ $f (x) = x^{2} + 1$ at $(- 2, 5)$ $(- 2, 5)$
86756	Find the Tangent Line at (-3,-57)	f(x)=7x-4x^2 at (-3,-57)	$f (x) = 7 x - 4 x^{2}$ $f (x) = 7 x - 4 x^{2}$ at $(- 3, - 57)$ $(- 3, - 57)$
86757	Find the Tangent Line at (5,10)	f(x) = square root of 5x+75 , (5,10)	$f (x) = \sqrt{5 x + 75}$ $f (x) = \sqrt{5 x + 75}$ , $(5, 10)$ $(5, 10)$
86758	Find the Tangent Line at (-2,1)	y^2=x^3-4x+1 at (-2,1)	$y^{2} = x^{3} - 4 x + 1$ $y^{2} = x^{3} - 4 x + 1$ at $(- 2, 1)$ $(- 2, 1)$
86759	Find the Tangent Line at x=10	f(x)=( natural log of x)^3 at x=10	$f (x) = \ln^{3} (x)$ $f (x) = \ln^{3} (x)$ at $x = 10$ $x = 10$
86760	Find the Tangent Line at x=-1	y=x^3 at x=-1	$y = x^{3}$ $y = x^{3}$ at $x = - 1$ $x = - 1$
86761	Find the Tangent Line at (1,3)	x^2+y^2=10 at (1,3)	$x^{2} + y^{2} = 10$ $x^{2} + y^{2} = 10$ at $(1, 3)$ $(1, 3)$
86762	Find the Tangent Line at x=-1	f(x)=-x^2-x+4 at x=-1	$f (x) = - x^{2} - x + 4$ $f (x) = - x^{2} - x + 4$ at $x = - 1$ $x = - 1$
86763	Find the Tangent Line at (0,1)	y^4+x^3=y^2+12x , tangent at (0,1)	$y^{4} + x^{3} = y^{2} + 12 x$ $y^{4} + x^{3} = y^{2} + 12 x$ , tangent at $(0, 1)$ $(0, 1)$
86764	Find the Tangent Line at (-3,-3)	(x+2)^2+(y-3)^2=37 , (-3,-3)	${(x + 2)}^{2} + {(y - 3)}^{2} = 37$ ${(x + 2)}^{2} + {(y - 3)}^{2} = 37$ , $(- 3, - 3)$ $(- 3, - 3)$
86765	Find the Tangent Line at (0,2)	y=2e^xcos(x) , (0,2)	$y = 2 e^{x} \cos (x)$ $y = 2 e^{x} \cos (x)$ , $(0, 2)$ $(0, 2)$
86766	Find the Tangent Line at (1,0)	f(x)=x-x^3 , (1,0)	$f (x) = x - x^{3}$ $f (x) = x - x^{3}$ , $(1, 0)$ $(1, 0)$
86767	Find the Tangent Line at (1,2)	f(x)=x^2+2x-1 , (1,2)	$f (x) = x^{2} + 2 x - 1$ $f (x) = x^{2} + 2 x - 1$ , $(1, 2)$ $(1, 2)$
86768	Find the Tangent Line at x=2	f(x)=( natural log of x)^5 at x=2	$f (x) = \ln^{5} (x)$ $f (x) = \ln^{5} (x)$ at $x = 2$ $x = 2$
86769	Find the Tangent Line at (5,7)	f(x) = square root of 5x+24 , (5,7)	$f (x) = \sqrt{5 x + 24}$ $f (x) = \sqrt{5 x + 24}$ , $(5, 7)$ $(5, 7)$
86770	Find the Tangent Line at (0,8)	8e^xcos(x) , (0,8)	$8 e^{x} \cos (x)$ $8 e^{x} \cos (x)$ , $(0, 8)$ $(0, 8)$
86771	Find the Tangent Line at (4,6)	g(x)=(3x)/(x-2) at (4,6)	$g (x) = \frac{3 x}{x - 2}$ $g (x) = \frac{3 x}{x - 2}$ at $(4, 6)$ $(4, 6)$
86772	Find the Tangent Line at x=-1	f(x)=1/6x^4 at x=-1	$f (x) = \frac{1}{6} x^{4}$ $f (x) = \frac{1}{6} x^{4}$ at $x = - 1$ $x = - 1$
86773	Find the Tangent Line at (-3,-9)	g(x)=(6x)/(x+5) at (-3,-9)	$g (x) = \frac{6 x}{x + 5}$ $g (x) = \frac{6 x}{x + 5}$ at $(- 3, - 9)$ $(- 3, - 9)$
86774	Find the Tangent Line at x=1	f(x) = square root of x+2/( square root of x) ; , x=1	$f (x) = \sqrt{x} + \frac{2}{\sqrt{x}}$ $f (x) = \sqrt{x} + \frac{2}{\sqrt{x}}$ ; , $x = 1$ $x = 1$
86775	Find the Tangent Line at (-3,0)	y=x^3-9x , (-3,0)	$y = x^{3} - 9 x$ $y = x^{3} - 9 x$ , $(- 3, 0)$ $(- 3, 0)$
86776	Find the Tangent Line at x=6	h(x)=7/x at x=6	$h (x) = \frac{7}{x}$ $h (x) = \frac{7}{x}$ at $x = 6$ $x = 6$
86777	Find the Tangent Line at (2,0)	y=x^3-4x , (2,0)	$y = x^{3} - 4 x$ $y = x^{3} - 4 x$ , $(2, 0)$ $(2, 0)$
86778	Find the Tangent Line at x=1	y = square root of x+3 at x=1	$y = \sqrt{x + 3}$ $y = \sqrt{x + 3}$ at $x = 1$ $x = 1$
86779	Find the Tangent Line at x=0	f(x)=x^3-3x^2+2x-2 at x=0	$f (x) = x^{3} - 3 x^{2} + 2 x - 2$ $f (x) = x^{3} - 3 x^{2} + 2 x - 2$ at $x = 0$ $x = 0$
86780	Find the Tangent Line at (0,0)	y=sin(8x)+sin(8x)^2 , (0,0)	$y = \sin (8 x) + \sin^{2} (8 x)$ $y = \sin (8 x) + \sin^{2} (8 x)$ , $(0, 0)$ $(0, 0)$
86781	Find the Tangent Line at x=-π/3	f(x)=sec(x)+1+(2 square root of 3pi)/3 at x=-pi/3	$f (x) = \sec (x) + 1 + \frac{2 \sqrt{3} π}{3}$ $f (x) = \sec (x) + 1 + \frac{2 \sqrt{3} π}{3}$ at $x = - \frac{π}{3}$ $x = - \frac{π}{3}$
86782	Find the Tangent Line at x=9	f(x)=( natural log of x)^2 at x=9	$f (x) = \ln^{2} (x)$ $f (x) = \ln^{2} (x)$ at $x = 9$ $x = 9$
86783	Find the Tangent Line at (2,16)	y=2x^3 , (2,16)	$y = 2 x^{3}$ $y = 2 x^{3}$ , $(2, 16)$ $(2, 16)$
86784	Find the Tangent Line at (7,14)	g(x)=(4x)/(x-5) at (7,14)	$g (x) = \frac{4 x}{x - 5}$ $g (x) = \frac{4 x}{x - 5}$ at $(7, 14)$ $(7, 14)$
86785	Find the Tangent Line at (-4,17)	f(x)=x^2+1 at (-4,17)	$f (x) = x^{2} + 1$ $f (x) = x^{2} + 1$ at $(- 4, 17)$ $(- 4, 17)$
86786	Find the Tangent Line at (5,1)	y=25/(x^2) at the point (5,1)	$y = \frac{25}{x^{2}}$ $y = \frac{25}{x^{2}}$ at the point $(5, 1)$ $(5, 1)$
86787	Find the Tangent Line at (-1,2)	f(x)=4x^2+2x , (-1,2)	$f (x) = 4 x^{2} + 2 x$ $f (x) = 4 x^{2} + 2 x$ , $(- 1, 2)$ $(- 1, 2)$
86788	Find the Tangent Line at x=10	f(x)=( natural log of x)^2 at x=10	$f (x) = \ln^{2} (x)$ $f (x) = \ln^{2} (x)$ at $x = 10$ $x = 10$
86789	Find the Tangent Line at (1,-1)	y=(-2x)/(x^2+1) at the origin and at the point (1,-1)	$y = \frac{- 2 x}{x^{2} + 1}$ $y = \frac{- 2 x}{x^{2} + 1}$ at the origin and at the point $(1, - 1)$ $(1, - 1)$
86790	Find the Tangent Line at (1,-1)	x^2y^3=y^2-2 ;, (1,-1)	$x^{2} y^{3} = y^{2} - 2$ $x^{2} y^{3} = y^{2} - 2$ ;, $(1, - 1)$ $(1, - 1)$
86791	Find the Tangent Line at (2,1)	3(x^2+y^2)^2=25(x^2-y^2) ; (2,1)	$3 {(x^{2} + y^{2})}^{2} = 25 (x^{2} - y^{2})$ $3 {(x^{2} + y^{2})}^{2} = 25 (x^{2} - y^{2})$ ; $(2, 1)$ $(2, 1)$
86792	Find the Tangent Line at x=3	f(x)=x^2-2 at x=3	$f (x) = x^{2} - 2$ $f (x) = x^{2} - 2$ at $x = 3$ $x = 3$
86793	Find the Tangent Line at (0,1)	y=e^(3x) , (0,1)	$y = e^{3 x}$ $y = e^{3 x}$ , $(0, 1)$ $(0, 1)$
86794	Find the Tangent Line at (6,6)	f(x) = square root of 6x at (6,6)	$f (x) = \sqrt{6 x}$ $f (x) = \sqrt{6 x}$ at $(6, 6)$ $(6, 6)$
86795	Find the Tangent Line at (2,16)	f(x)=x^4 , (2,16)	$f (x) = x^{4}$ $f (x) = x^{4}$ , $(2, 16)$ $(2, 16)$
86796	Find the Tangent Line at x=1/25	f(x) = square root of x , x=1/25	$f (x) = \sqrt{x}$ $f (x) = \sqrt{x}$ , $x = \frac{1}{25}$ $x = \frac{1}{25}$
86797	Find the Tangent Line at (3,3)	f(x) = square root of 3x at (3,3)	$f (x) = \sqrt{3 x}$ $f (x) = \sqrt{3 x}$ at $(3, 3)$ $(3, 3)$
86798	Find the Tangent Line at (2,1)	x^2+4xy+y^2=13 , (2,1)	$x^{2} + 4 x y + y^{2} = 13$ $x^{2} + 4 x y + y^{2} = 13$ , $(2, 1)$ $(2, 1)$
86799	Find the Tangent Line at x=2	y=x^2 , x=2	$y = x^{2}$ $y = x^{2}$ , $x = 2$ $x = 2$
86800	Find the Tangent Line at (3,19)	y=x^3-3x+1 , (3,19)	$y = x^{3} - 3 x + 1$ $y = x^{3} - 3 x + 1$ , $(3, 19)$ $(3, 19)$