Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2101	Evaluate the Limit	limit as x approaches 225 of ( square root of x-15)/(x-225)	$lim_{x \to 225} \frac{\sqrt{x} - 15}{x - 225}$
2102	Find the Derivative - d/dx	f(x)=sin(2x)	$f (x) = \sin (2 x)$
2103	Find the Derivative - d/dx	f(x)=sin(3x)	$f (x) = \sin (3 x)$
2104	Find the Derivative - d/dx	(x^3)/6	$\frac{x^{3}}{6}$
2105	Find the Derivative - d/dx	3x^2-4x+1	$3 x^{2} - 4 x + 1$
2106	Find the Derivative - d/dx	y=x^3-3x+1	$y = x^{3} - 3 x + 1$
2107	Find the Derivative - d/dx	tan( square root of x)	$\tan (\sqrt{x})$
2108	Find the Derivative - d/dx	arcsec(x)	$arcsec (x)$
2109	Find the Derivative - d/dx	tan(x)sec(x)	$\tan (x) \sec (x)$
2110	Find the Derivative - d/dx	25-x^2	$25 - x^{2}$
2111	Find the Derivative - d/dx	x(3x-9)^3	$x {(3 x - 9)}^{3}$
2112	Find the Derivative - d/dx	natural log of cos(h(x))	$\ln (\cosh (x))$
2113	Find the Derivative - d/dx	8/x-2/(x^3)+1/(x^4)	$\frac{8}{x} - \frac{2}{x^{3}} + \frac{1}{x^{4}}$
2114	Find the Derivative - d/dx	natural log of x-1	$\ln (x - 1)$
2115	Find the Derivative - d/dx	natural log of xy	$\ln (x y)$
2116	Find the Derivative - d/dx	6x-x^2	$6 x - x^{2}$
2117	Find the Derivative - d/dx	xcos(2x)	$x \cos (2 x)$
2118	Find the Derivative - d/dx	arctan(cos(x))	$\arctan (\cos (x))$
2119	Find the Derivative - d/dx	1/(x^11)	$\frac{1}{x^{11}}$
2120	Find the Derivative - d/dx	4e^(-x)	$4 e^{- x}$
2121	Find the Derivative - d/dx	f(x)=0	$f (x) = 0$
2122	Find the Derivative - d/dx	f(x)=4^x	$f (x) = 4^{x}$
2123	Find the Derivative - d/dx	f(x)=e^(4x)	$f (x) = e^{4 x}$
2124	Find the Derivative - d/dx	f(x)=e^(1/x)	$f (x) = e^{\frac{1}{x}}$
2125	Find the Derivative - d/dx	f(x)=(sin(x))/(cos(x))	$f (x) = \frac{\sin (x)}{\cos (x)}$
2126	Find the Derivative - d/d@VAR	f(x)=x^2+5	$f (x) = x^{2} + 5$
2127	Find the Derivative - d/d@VAR	f(x)=x^12	$f (x) = x^{12}$
2128	Find the Derivative - d/d@VAR	f(x)=x^2-2x	$f (x) = x^{2} - 2 x$
2129	Find the Derivative - d/d@VAR	f(x)=x^2-1	$f (x) = x^{2} - 1$
2130	Find the Derivative - d/d@VAR	f(x)=4-x^2	$f (x) = 4 - x^{2}$
2131	Factor	12x^2-18x-12	$12 x^{2} - 18 x - 12$
2132	Factor	t^2+8	$t^{2} + 8$
2133	Find the Integral	cos(3x)	$\cos (3 x)$
2134	Find dy/dx	2x^2-y^2=5	$2 x^{2} - y^{2} = 5$
2135	Find dy/dx	xy^2-x^3y=6	$x y^{2} - x^{3} y = 6$
2136	Find dy/dx	x^3-3x^2y+2xy^2=12	$x^{3} - 3 x^{2} y + 2 x y^{2} = 12$
2137	Find dy/dx	24x^3y^2-8y^3=-11	$24 x^{3} y^{2} - 8 y^{3} = - 11$
2138	Find dy/dx	tan(4x+y)=4x	$\tan (4 x + y) = 4 x$
2139	Find dy/dx	xy+2x+3y=1	$x y + 2 x + 3 y = 1$
2140	Find dy/dx	x^2y^2-2x=3	$x^{2} y^{2} - 2 x = 3$
2141	Find the Derivative - d/dx	y=x^9e^x	$y = x^{9} e^{x}$
2142	Evaluate the Limit	limit as x approaches -4 of (1/4+1/x)/(4+x)	$lim_{x \to - 4} \frac{\frac{1}{4} + \frac{1}{x}}{4 + x}$
2143	Find the Derivative - d/dx	x^2-6	$x^{2} - 6$
2144	Find dy/dx	2x^3-3y^2=8	$2 x^{3} - 3 y^{2} = 8$
2145	Find dy/dx	(x+2)^2+(y-3)^2=37	${(x + 2)}^{2} + {(y - 3)}^{2} = 37$
2146	Find dy/dx	sin(x+y)=y^2cos(x)	$\sin (x + y) = y^{2} \cos (x)$
2147	Evaluate the Limit	limit as x approaches 0 of ((2+x)^3-8)/x	$lim_{x \to 0} \frac{{(2 + x)}^{3} - 8}{x}$
2148	Find the Derivative - d/dx	10x^5-8x+6e^x-10	$10 x^{5} - 8 x + 6 e^{x} - 10$
2149	Find dy/dx	y square root of x+1=4	$y \sqrt{x + 1} = 4$
2150	Find dy/dx	ycos(x)=3x^2+4y^2	$y \cos (x) = 3 x^{2} + 4 y^{2}$
2151	Find dy/dx	ycos(x)=4x^2+5y^2	$y \cos (x) = 4 x^{2} + 5 y^{2}$
2152	Find the Derivative - d/dx	y=-csc(x)-cos(x)	$y = - \csc (x) - \cos (x)$
2153	Find the Derivative - d/dx	natural log of 10	$\ln (10)$
2154	Find the Derivative - d/dx	xe^(-x^2)	$x e^{- x^{2}}$
2155	Find the Derivative - d/dx	4x^(-3/8)	$4 x^{- \frac{3}{8}}$
2156	Find the Derivative - d/dx	2^5*0	$2^{50}$
2157	Find dy/dx	y=sin(x+y)	$y = \sin (x + y)$
2158	Find dy/dx	ycos(x)=x^2+y^2	$y \cos (x) = x^{2} + y^{2}$
2159	Evaluate the Limit	limit as x approaches -10 of (x^2-100)/(x+10)	$lim_{x \to - 10} \frac{x^{2} - 100}{x + 10}$
2160	Find dy/dx	y=x^2e^x	$y = x^{2} e^{x}$
2161	Find the Derivative - d/dx	2x^2+3x	$2 x^{2} + 3 x$
2162	Find the Derivative - d/dx	(7x+1)^2	${(7 x + 1)}^{2}$
2163	Find the Derivative - d/dx	-1/3(x^-3-x^6)	$- \frac{1}{3} (x^{- 3} - x^{6})$
2164	Find the Derivative - d/dx	5xe^x	$5 x e^{x}$
2165	Find the Derivative - d/dx	y=(x^2-1)/(x^2+x+1)	$y = \frac{x^{2} - 1}{x^{2} + x + 1}$
2166	Find the Derivative - d/dx	(x^2+4x+3)/( square root of x)	$\frac{(x^{2} + 4 x + 3)}{\sqrt{x}}$
2167	Find the Derivative - d/dx	y=x^10e^x	$y = x^{10} e^{x}$
2168	Find the Derivative - d/dx	cos(6x)	$\cos (6 x)$
2169	Find the 2nd Derivative	f(x)=xsin(x)	$f (x) = x \sin (x)$
2170	Find the 2nd Derivative	3e^(-x^2)	$3 e^{- x^{2}}$
2171	Evaluate the Summation	sum from i=1 to 5 of (2/3)^(i+1)	$\sum_{i = 1}^{5} {(\frac{2}{3})}^{i + 1}$
2172	Evaluate the Summation	sum from i=1 to 6 of 3i+2	$\sum_{i = 1}^{6} 3 i + 2$
2173	Evaluate the Summation	sum from n=1 to 7 of 2(-2)^(n-1)	$\sum_{n = 1}^{7} 2 {(- 2)}^{n - 1}$
2174	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of sin(x) natural log of x	$lim_{x \to 0} \sin (x) \ln (x)$
2175	Evaluate Using L'Hospital's Rule	limit as x approaches 8 of x^3e^(-x^2)	$lim_{x \to 8} x^{3} e^{- x^{2}}$
2176	Evaluate the Integral	integral of (e^(tan(x)))/(cos(x)^2) with respect to x	$\int \frac{e^{\tan (x)}}{\cos^{2} (x)} d x$
2177	Evaluate the Integral	integral of (e^u)/((1-e^u)^2) with respect to u	$\int \frac{e^{u}}{{(1 - e^{u})}^{2}} d u$
2178	Evaluate the Integral	integral of (( natural log of x)^4)/x with respect to x	$\int \frac{\ln^{4} (x)}{x} d x$
2179	Evaluate the Integral	integral of (( natural log of x)^5)/x with respect to x	$\int \frac{\ln^{5} (x)}{x} d x$
2180	Evaluate the Integral	integral of (( natural log of x)^3)/x with respect to x	$\int \frac{\ln^{3} (x)}{x} d x$
2181	Evaluate the Integral	integral of ( square root of t^6+5t)(6t^5+5) with respect to t	$\int (\sqrt{t^{6} + 5 t}) (6 t^{5} + 5) d t$
2182	Evaluate the Integral	integral of 1/( square root of x^3)+5e^(5x) with respect to x	$\int \frac{1}{\sqrt{x^{3}}} + 5 e^{5 x} d x$
2183	Evaluate the Integral	integral of 5x-7 with respect to x	$\int 5 x - 7 d x$
2184	Evaluate the Integral	integral of 3x-7 with respect to x	$\int 3 x - 7 d x$
2185	Evaluate the Integral	integral of 9x^2+2x-3 with respect to x	$\int 9 x^{2} + 2 x - 3 d x$
2186	Evaluate the Integral	integral of 8x^3-9x^2+4 with respect to x	$\int 8 x^{3} - 9 x^{2} + 4 d x$
2187	Evaluate the Integral	integral of 1-csc(x)cot(x) with respect to x	$\int 1 - \csc (x) \cot (x) d x$
2188	Evaluate the Integral	integral of 2x-3 with respect to x	$\int 2 x - 3 d x$
2189	Evaluate the Integral	integral of (2+2x)e^(4x+2x^2) with respect to x	$\int (2 + 2 x) e^{4 x + 2 x^{2}} d x$
2190	Evaluate the Integral	integral of 3x^5-8x^3+2 with respect to x	$\int 3 x^{5} - 8 x^{3} + 2 d x$
2191	Find the 2nd Derivative	y=tan(x)	$y = \tan (x)$
2192	Simplify	e^negative infinity	$e^{- \infty}$
2193	Find dy/dx	x^(2/3)+y^(2/3)=4	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$
2194	Evaluate the Integral	integral of 1/(5x+4) with respect to x	$\int \frac{1}{5 x + 4} d x$
2195	Evaluate the Integral	integral of 1/(5x^3) with respect to x	$\int \frac{1}{5 x^{3}} d x$
2196	Evaluate the Integral	integral of 1/(3x^2) with respect to x	$\int \frac{1}{3 x^{2}} d x$
2197	Evaluate the Integral	integral of 1/(3x^5) with respect to x	$\int \frac{1}{3 x^{5}} d x$
2198	Evaluate the Integral	integral of 1/(x natural log of x^4) with respect to x	$\int \frac{1}{x \ln (x^{4})} d x$
2199	Evaluate the Integral	integral of 1/(1-sin(x)) with respect to x	$\int \frac{1}{1 - \sin (x)} d x$
2200	Evaluate the Integral	integral of 1/(1+4x^2) with respect to x	$\int \frac{1}{1 + 4 x^{2}} d x$