Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
7001	Simplify	cot(arcsin(-( square root of 3)/2))	$\cot (\arcsin (- \frac{\sqrt{3}}{2}))$
7002	Simplify	3 cube root of x	$3 \sqrt[3]{x}$
7003	Simplify	5arctan(x- square root of 1+x^2)	$5 \arctan (x - \sqrt{1 + x^{2}})$
7004	Simplify	2x square root of x	$2 x \sqrt{x}$
7005	Simplify	cube root of 81x^5y^10 cube root of 9xy^2	$\sqrt[3]{81 x^{5} y^{10}} \sqrt[3]{9 x y^{2}}$
7006	Simplify	(x+2)/(x^3+8)	$\frac{x + 2}{x^{3} + 8}$
7007	Find the Derivative Using Quotient Rule - d/dx	y=2/(2x^4-5)	$y = \frac{2}{2 x^{4} - 5}$
7008	Find the Derivative Using Quotient Rule - d/dx	y=(x^2+4x+3)/( square root of x)	$y = \frac{x^{2} + 4 x + 3}{\sqrt{x}}$
7009	Find the Derivative Using Quotient Rule - d/dx	f(x)=(cos(x))/(x^3)	$f (x) = \frac{\cos (x)}{x^{3}}$
7010	Find the Derivative Using Quotient Rule - d/dx	(8x+7)/( square root of x)	$\frac{8 x + 7}{\sqrt{x}}$
7011	Find the Derivative Using Quotient Rule - d/dx	(cos(x))/(sin(x))	$\frac{\cos (x)}{\sin (x)}$
7012	Find the Derivative Using Quotient Rule - d/d@VAR	f(x)=(3x^2-5x)/(x^2+1)	$f (x) = \frac{3 x^{2} - 5 x}{x^{2} + 1}$
7013	Find the Derivative Using Quotient Rule - d/d@VAR	f(x)=(5x-7)/(x^2-2)	$f (x) = \frac{5 x - 7}{x^{2} - 2}$
7014	Find the Derivative Using Quotient Rule - d/dx	(x^2)/(x-1)	$\frac{x^{2}}{x - 1}$
7015	Find the Derivative Using Product Rule - d/d@VAR	f(x)=x^9cos(x)	$f (x) = x^{9} \cos (x)$
7016	Find the Derivative Using Product Rule - d/dr	4/3*(pr^3)	$\frac{4}{3} \cdot (p r^{3})$
7017	Find the Derivative Using Product Rule - d/d@VAR	h(x)=7x^2(6x+5^2)	$h (x) = 7 x^{2} (6 x + 5^{2})$
7018	Find the Derivative Using Chain Rule - d/dx	y=((x+5)^5-1)^4	$y = {({(x + 5)}^{5} - 1)}^{4}$
7019	Find the Derivative Using Chain Rule - d/dy	sin(x+y)	$\sin (x + y)$
7020	Find the Derivative Using Chain Rule - d/dx	y=sec(x^2)	$y = \sec (x^{2})$
7021	Find the Derivative Using Chain Rule - d/dx	y=sin( square root of x)	$y = \sin (\sqrt{x})$
7022	Find the Derivative Using Chain Rule - d/dx	y=x natural log of x	$y = x \ln (x)$
7023	Find the x and y Intercepts	f(x)=x^3-8x^2-20x	$f (x) = x^{3} - 8 x^{2} - 20 x$
7024	Find the x and y Intercepts	f(x)=2x	$f (x) = 2 x$
7025	Find the x and y Intercepts	f(x) = natural log of x^2+25	$f (x) = \ln (x^{2} + 25)$
7026	Find the x and y Intercepts	f(x)=x^3-18x^2+81x	$f (x) = x^{3} - 18 x^{2} + 81 x$
7027	Find the x and y Intercepts	f(x)=x^3+6x^2+9x	$f (x) = x^{3} + 6 x^{2} + 9 x$
7028	Find the x and y Intercepts	f(x)=(sin(4x))/(2x)	$f (x) = \frac{\sin (4 x)}{2 x}$
7029	Find the x and y Intercepts	f(x)=-3/(x-4)	$f (x) = \frac{- 3}{x - 4}$
7030	Find the x and y Intercepts	y=x square root of 5-x^2	$y = x \sqrt{5 - x^{2}}$
7031	Find the x and y Intercepts	x^4-6x^2	$x^{4} - 6 x^{2}$
7032	Find dr/d?	r=tan(x)sec(x)	$r = \tan (x) \sec (x)$
7033	Find dr/ds	r=1/(2s)-8/(5s^4)	$r = \frac{1}{2 s} - \frac{8}{5 s^{4}}$
7034	Find dr/ds	r=1/(3s^2)-5/(2s)	$r = \frac{1}{3 s^{2}} - \frac{5}{2 s}$
7035	Find dP/dx	(dP)/(dx)=200x^1.075	$\frac{d P}{d x} = 200 x^{1.075}$
7036	Find ds/dt	s=4t^3-3t^4	$s = 4 t^{3} - 3 t^{4}$
7037	Find ds/dt	s=t^7 natural log of t	$s = t^{7} \ln (t)$
7038	Find ds/dt	s=t^5 natural log of t	$s = t^{5} \ln (t)$
7039	Find ds/dt	s=t^3-3t	$s = t^{3} - 3 t$
7040	Find dr/dw	r=(4e^w)/(5w)	$r = \frac{4 e^{w}}{5 w}$
7041	Find dv/dt	v=2t^2+8t+12	$v = 2 t^{2} + 8 t + 12$
7042	Find dV/ds	V=s^3	$V = s^{3}$
7043	Find dV/dt	V=4/(t+6)	$V = \frac{4}{t + 6}$
7044	Find du/dv	u=v^2 square root of 2v-9	$u = v^{2} \sqrt{2 v - 9}$
7045	Find ds/dt	s=72+64t-16t^2	$s = 72 + 64 t - 16 t^{2}$
7046	Find dt/ds	s=32+64t-16t^2	$s = 32 + 64 t - 16 t^{2}$
7047	Find dt/dx	t=2/(x+3)	$t = \frac{2}{x + 3}$
7048	Evaluate the Limit	limit as x approaches infinity of e^(-x^2)	$lim_{x \to \infty} e^{- x^{2}}$
7049	Evaluate the Limit	limit as h approaches 0 of (2.8^h-1)/h	$lim_{h \to 0} \frac{{2.8}^{h} - 1}{h}$
7050	Find dx/dt	x=t(3t+1)^2	$x = t {(3 t + 1)}^{2}$
7051	Find dx/dy	x^2y+e^(2x+y)=2x square root of y	$x^{2} y + e^{2 x + y} = 2 x \sqrt{y}$
7052	Find the x and y Intercepts	y=x^9-9x	$y = x^{9} - 9 x$
7053	Find the x and y Intercepts	y=x^3+3x^2+3x+2	$y = x^{3} + 3 x^{2} + 3 x + 2$
7054	Find the x and y Intercepts	y=x^3-3x^2-105x	$y = x^{3} - 3 x^{2} - 105 x$
7055	Find the x and y Intercepts	y=x^3-6x^2-15x+4	$y = x^{3} - 6 x^{2} - 15 x + 4$
7056	Find dp/dq	pi=(sec(q)+csc(q))/(csc(q))	$π = \frac{\sec (q) + \csc (q)}{\csc (q)}$
7057	Find dc/dk	c=7/(k^3)	$c = \frac{7}{k^{3}}$
7058	Find the Derivative Using Chain Rule - d/dt	t(2t+1)^2	$t {(2 t + 1)}^{2}$
7059	Find the Derivative Using Chain Rule - d/d?	sec(x)tan(x)	$\sec (x) \tan (x)$
7060	Find the Derivative Using Chain Rule - d/df	(f(x)*1)/( square root of 3x-2)	$\frac{f (x) \cdot 1}{\sqrt{3 x - 2}}$
7061	Find the Derivative Using Chain Rule - d/d@VAR	G(r) = square root of r+ seventh root of r	$G (r) = \sqrt{r} + \sqrt[7]{r}$
7062	Find the Derivative Using Chain Rule - d/dx	x/(e^x)	$\frac{x}{e^{x}}$
7063	Find the Derivative Using Chain Rule - d/dx	sin(pix)^2	$\sin^{2} (π x)$
7064	Find the Derivative Using Chain Rule - d/dx	1/(x^3)	$\frac{1}{x^{3}}$
7065	Find the Derivative Using Chain Rule - d/dv	(v^-3+5v^-2)^3	${(v^{- 3} + 5 v^{- 2})}^{3}$
7066	Find the Integral	-2/(x^2)	$- \frac{2}{x^{2}}$
7067	Find the Integral	1/(7 seventh root of x^6)	$\frac{1}{7 \sqrt[7]{x^{6}}}$
7068	Find the Integral	(x^2)/(x^2+5)	$\frac{x^{2}}{x^{2} + 5}$
7069	Find the Integral	(-x^3+17x^2-12x-9)/(x^4-3x^3)	$\frac{- x^{3} + 17 x^{2} - 12 x - 9}{x^{4} - 3 x^{3}}$
7070	Find the Integral	(x^3-x^2+1)/(x-1)	$\frac{x^{3} - x^{2} + 1}{x - 1}$
7071	Find the Integral	1/(e^(x^2))	$\frac{1}{e^{x^{2}}}$
7072	Find the Integral	1/( square root of 1-x^2)	$\frac{1}{\sqrt{1 - x^{2}}}$
7073	Find the Integral	1/(x^6)	$\frac{1}{x^{6}}$
7074	Find the Integral	1/2x^2	$\frac{1}{2} x^{2}$
7075	Find the Integral	1/2*cos(2x)	$\frac{1}{2} \cdot \cos (2 x)$
7076	Find the Integral	square root of 4-x^2	$\sqrt{4 - x^{2}}$
7077	Find the Integral	square root of 4	$\sqrt{4}$
7078	Find the Integral	square root of 14	$\sqrt{14}$
7079	Find the Integral	square root of 10	$\sqrt{10}$
7080	Find the Integral	square root of 2	$\sqrt{2}$
7081	Find the Integral	(f(-1)-f*-2)/((-1)-(-2))	$\frac{f (- 1) - f \cdot - 2}{(- 1) - (- 2)}$
7082	Find the Integral	arctan(- square root of 3)	$\arctan (- \sqrt{3})$
7083	Find the Integral	u^(-1/2)	$u^{- \frac{1}{2}}$
7084	Find the Integral	9/( square root of 1-x^2)	$\frac{9}{\sqrt{1 - x^{2}}}$
7085	Find the Integral	(5+t+t^2)/( square root of t)	$\frac{5 + t + t^{2}}{\sqrt{t}}$
7086	Find the Integral	6/( square root of x)	$\frac{6}{\sqrt{x}}$
7087	Find the Integral	e^(-a^2)	$e^{- a^{2}}$
7088	Find the Integral	2x-5	$2 x - 5$
7089	Find the Integral	2x-6	$2 x - 6$
7090	Find the Integral	2y	$2 y$
7091	Find the Integral	25x^(3/2)	$25 x^{\frac{3}{2}}$
7092	Find the Integral	25-x^2	$25 - x^{2}$
7093	Find the Integral	16-x^2	$16 - x^{2}$
7094	Find the Integral	4-x^2	$4 - x^{2}$
7095	Find the Integral	3x-4	$3 x - 4$
7096	Find the Integral	3x-6	$3 x - 6$
7097	Find the Integral	5e^(4x)	$5 e^{4 x}$
7098	Find the Integral	5x^4	$5 x^{4}$
7099	Find the Integral	10x	$10 x$
7100	Find the Integral	x^2cos(x)	$x^{2} \cos (x)$