Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
69101	Find dy/dx	y^2=5x^4-x^2	$y^{2} = 5 x^{4} - x^{2}$
69102	Evaluate the Integral	integral from -1 to 2 of (x^3-4x) with respect to x	$\int_{- 1}^{2} (x^{3} - 4 x) d x$
69103	Evaluate the Integral	integral of e^(3+2x) with respect to x	$\int e^{3 + 2 x} d x$
69104	Find the Horizontal Tangent Line	f(x)=e^xcos(x)	$f (x) = e^{x} \cos (x)$
69105	Evaluate the Limit	limit as x approaches 2/3 of (27x^3-8)/(9x^2-4)	$lim_{x \to \frac{2}{3}} \frac{27 x^{3} - 8}{9 x^{2} - 4}$
69106	Find dy/dx	tan(xy)=x+y	$\tan (x y) = x + y$
69107	Evaluate the Integral	integral from -1 to 1 of (x^2-x)/x with respect to x	$\int_{- 1}^{1} \frac{x^{2} - x}{x} d x$
69108	Find the Derivative - d/dx	-(e^(-2x^3))/(4x^4)	$- \frac{e^{- 2 x^{3}}}{4 x^{4}}$
69109	Find the Derivative - d/dx	( limit as h approaches 0 of f(x+h)-fx)/h	$\frac{lim_{h \to 0} f (x + h) - f x}{h}$
69110	Find the Linearization at a=125	f(x) = cube root of x , a=125	$f (x) = \sqrt[3]{x}$ , $a = 125$
69111	Evaluate the Limit	limit as x approaches infinity of (x^3)/(9e^(x/5))	$lim_{x \to \infty} \frac{x^{3}}{9 e^{\frac{x}{5}}}$
69112	Find the Derivative - d/dx	1/2e^x	$\frac{1}{2} e^{x}$
69113	Find the Slope	f(x)=x	$f (x) = x$
69114	Find Where Increasing/Decreasing	f(x)=-(1/2)^x	$f (x) = - {(\frac{1}{2})}^{x}$
69115	Find the Derivative - d/dx	d/(dx)((x^3)/(sin(x)))	$\frac{d}{d x} (\frac{x^{3}}{\sin (x)})$
69116	Find dy/dx	y=( natural log of x)^( natural log of x)	$y = {(\ln (x))}^{\ln (x)}$
69117	Evaluate the Limit	limit as x approaches -1 of (x+x^2+x^3)^135	$lim_{x \to - 1} {(x + x^{2} + x^{3})}^{135}$
69118	Find the Derivative - d/dx	y=x/(sin(x))	$y = \frac{x}{\sin (x)}$
69119	Evaluate the Limit	limit as x approaches infinity of 3-x+(x^2-2x)/(x+5)	$lim_{x \to \infty} 3 - x + \frac{x^{2} - 2 x}{x + 5}$
69120	Find the Tangent Line at (2,-4)	y=4x-3x^2 , (2,-4)	$y = 4 x - 3 x^{2}$ , $(2, - 4)$
69121	Evaluate the Integral	integral of x^2cos(1/2x) with respect to x	$\int x^{2} \cos (\frac{1}{2} x) d x$
69122	Evaluate the Integral	integral from 0 to 5 of 7* cube root of x^2 with respect to x	$\int_{0}^{5} 7 \cdot \sqrt[3]{x^{2}} d x$
69123	Find the Center and Radius	4x^2+y^2=16	$4 x^{2} + y^{2} = 16$
69124	Find the Derivative - d/dx	d/(dx)( square root of 49x^-9)	$\frac{d}{d x} (\sqrt{49 x^{- 9}})$
69125	Find dy/dx	y=(cos(x))/(1+sin(x))	$y = \frac{\cos (x)}{1 + \sin (x)}$
69126	Integrate By Parts	integral of x^2e^(x^3) with respect to x	$\int x^{2} e^{x^{3}} d x$
69127	Find the Derivative - d/dx	d/(dx)(5sin(x)+x^2)	$\frac{d}{d x} (5 \sin (x) + x^{2})$
69128	Evaluate the Limit	limit as x approaches 0 of (x^2+x)/(x^2-4x)	$lim_{x \to 0} \frac{x^{2} + x}{x^{2} - 4 x}$
69129	Find Where Increasing/Decreasing	f(x)=5/3x^3-15/2x^2	$f (x) = \frac{5}{3} x^{3} - \frac{15}{2} x^{2}$
69130	Evaluate the Integral	integral of (6x^6+3x^5+5x-4) with respect to x	$\int (6 x^{6} + 3 x^{5} + 5 x - 4) d x$
69131	Find the Derivative - d/dx	y = natural log of x+ square root of x^2+1	$y = \ln (x + \sqrt{x^{2} + 1})$
69132	Find the Maximum/Minimum Value	y=-3x^2	$y = - 3 x^{2}$
69133	Find dy/dx	x^2+4xy+y^2=13	$x^{2} + 4 x y + y^{2} = 13$
69134	Find dy/dx	y^6=x^7	$y^{6} = x^{7}$
69135	Find the Tangent Line at (7,0)	y = natural log of x^2-7x+1 , (7,0)	$y = \ln (x^{2} - 7 x + 1)$ , $(7, 0)$
69136	Find the Derivative - d/dx	3/2x^(1/2)	$\frac{3}{2} x^{\frac{1}{2}}$
69137	Evaluate the Integral	integral from 2 to 5 of (-3v+4) with respect to v	$\int_{2}^{5} (- 3 v + 4) d v$
69138	Evaluate the Integral	integral from 0 to 3 of (9-x^2) with respect to x	$\int_{0}^{3} (9 - x^{2}) d x$
69139	Evaluate the Limit	limit as x approaches negative infinity of (3x^2+1)/(5-2x)	$lim_{x \to - \infty} \frac{3 x^{2} + 1}{5 - 2 x}$
69140	Find the Derivative - d/dx	y=( square root of x)^(3x)	$y = {(\sqrt{x})}^{3 x}$
69141	Find the Maximum/Minimum Value	f(x)=6x^(2/3)-4x	$f (x) = 6 x^{\frac{2}{3}} - 4 x$
69142	Evaluate the Limit	limit as x approaches 0 of ( square root of 1+x-1)/( cube root of 1+x-1)	$lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{\sqrt[3]{1 + x} - 1}$
69143	Find the Derivative - d/dx	(x-3)/2	$\frac{x - 3}{2}$
69144	Evaluate the Integral	integral from 0 to 1 of (x^2+ square root of x) with respect to x	$\int_{0}^{1} (x^{2} + \sqrt{x}) d x$
69145	Find the Antiderivative	square root of 3	$\sqrt{3}$
69146	Find dy/dx	y=sin(x+y)	$y = \sin (x + y)$
69147	Evaluate the Integral	integral of (6x^2-5x+3) with respect to x	$\int (6 x^{2} - 5 x + 3) d x$
69148	Evaluate the Limit	limit as x approaches 2 of ( square root of 2x- square root of 6-x)/(4-x^2)	$lim_{x \to 2} \frac{\sqrt{2 x} - \sqrt{6 - x}}{4 - x^{2}}$
69149	Find dy/dx	1/x+1/y=2	$\frac{1}{x} + \frac{1}{y} = 2$
69150	Find dy/dx	x^2y-2x^2-8=0	$x^{2} y - 2 x^{2} - 8 = 0$
69151	Find the Tangent Line at (1/2,π/2)	y=3arcsin(x) , (1/2,pi/2)	$y = 3 \arcsin (x)$ , $(\frac{1}{2}, \frac{π}{2})$
69152	Find dy/dx	x^2y^2-2x=3	$x^{2} y^{2} - 2 x = 3$
69153	Evaluate the Limit	limit as x approaches infinity of (8x^2-5)/(3x^2+x-3)	$lim_{x \to \infty} \frac{8 x^{2} - 5}{3 x^{2} + x - 3}$
69154	Find dy/dx	e^y-y^2=4x	$e^{y} - y^{2} = 4 x$
69155	Find the Derivative - d/dx	y=-7/x-5/x+1/x	$y = - \frac{7}{x} - \frac{5}{x} + \frac{1}{x}$
69156	Find the Derivative - d/dx	y=1/( cube root of (5-x^3)^5)	$y = \frac{1}{\sqrt[3]{{(5 - x^{3})}^{5}}}$
69157	Evaluate the Integral	integral of 1/2(3^x) with respect to x	$\int \frac{1}{2} (3^{x}) d x$
69158	Find dy/dx	x^2y^2=49	$x^{2} y^{2} = 49$
69159	Find the Derivative - d/dx	(-sin(x))	$(- \sin (x))$
69160	Evaluate the Limit	limit as x approaches 1 of (x^2- square root of x)/( square root of x-1)	$lim_{x \to 1} \frac{x^{2} - \sqrt{x}}{\sqrt{x} - 1}$
69161	Find the Maximum/Minimum Value	f(x)=(x^2)/(x-2)	$f (x) = \frac{x^{2}}{x - 2}$
69162	Evaluate the Summation	sum from i=1 to 50 of 2n-3	$\sum_{i = 1}^{50} 2 n - 3$
69163	Integrate Using Trig Substitution	integral of ( square root of x^2-9)/x with respect to x	$\int \frac{\sqrt{x^{2} - 9}}{x} d x$
69164	Evaluate the Limit	limit as x approaches -5 of (1/(-3x-8)-1/7)/(1/(-3x-9)-1/6)	$lim_{x \to - 5} \frac{\frac{1}{- 3 x - 8} - \frac{1}{7}}{\frac{1}{- 3 x - 9} - \frac{1}{6}}$
69165	Find the Derivative - d/dx	y = cube root of x(2+x)	$y = \sqrt[3]{x} (2 + x)$
69166	Find dy/dx	y = square root of 8x	$y = \sqrt{8 x}$
69167	Evaluate the Integral	integral of square root of 2x^3+7x^2 with respect to x	$\int \sqrt{2 x^{3} + 7} x^{2} d x$
69168	Find the Derivative - d/dx	y=(2x^2+x-3)/x	$y = \frac{2 x^{2} + x - 3}{x}$
69169	Find the Antiderivative	1/( square root of 2x)	$\frac{1}{\sqrt{2 x}}$
69170	Eliminate the Parameter	x=t^3+t+4 , y=-2t^3-2t	$x = t^{3} + t + 4$ , $y = - 2 t^{3} - 2 t$
69171	Find the Derivative - d/dx	y=x^5+5x^4-10x^2+6	$y = x^{5} + 5 x^{4} - 10 x^{2} + 6$
69172	Find dy/dx	y=(x+1)^2(x^2+1)^-3	$y = {(x + 1)}^{2} {(x^{2} + 1)}^{- 3}$
69173	Find the Derivative - d/dy	1/(x+y)	$\frac{1}{x + y}$
69174	Use Logarithmic Differentiation to Find the Derivative	y=sin(9x)^( natural log of x)	$y = {\sin (9 x)}^{\ln (x)}$
69175	Evaluate the Integral	integral of (2 square root of t-t-9/(t^2)) with respect to t	$\int (2 \sqrt{t} - t - \frac{9}{t^{2}}) d t$
69176	Find dy/dx	y=(2x+5)/(3x-2)	$y = \frac{2 x + 5}{3 x - 2}$
69177	Find dy/dx	y^2-2y=x	$y^{2} - 2 y = x$
69178	Find dx/dy	y=x^(sin(x))	$y = x^{\sin (x)}$
69179	Find the Tangent Line at (16,64)	y=16 square root of x , (16,64)	$y = 16 \sqrt{x}$ , $(16, 64)$
69180	Find dy/dx	x^3y^2=2x^2+y^2	$x^{3} y^{2} = 2 x^{2} + y^{2}$
69181	Find the Derivative - d/dx	d/(dx)e^(3x)	$\frac{d}{d x} e^{3 x}$
69182	Evaluate the Limit	limit as y approaches negative infinity of (2-y)/( square root of 7+6y^2)	$lim_{y \to - \infty} \frac{2 - y}{\sqrt{7 + 6 y^{2}}}$
69183	Evaluate the Limit	limit as x approaches 3 of (x^3+2)(x^2-5x)	$lim_{x \to 3} (x^{3} + 2) (x^{2} - 5 x)$
69184	Evaluate the Limit	limit as x approaches 0 of (cos(x)-sin(x)-1)/(2x)	$lim_{x \to 0} \frac{\cos (x) - \sin (x) - 1}{2 x}$
69185	Find the Tangent Line at (2,1)	x^2+6xy+12y^2=28 , (2,1)	$x^{2} + 6 x y + 12 y^{2} = 28$ , $(2, 1)$
69186	Find dy/dx	cos(y)=x	$\cos (y) = x$
69187	Find the Derivative - d/dx	y=arcsinh(tan(x))	$y = arcsinh (\tan (x))$
69188	Evaluate the Integral	e^( integral of -2/x with respect to x)	$e^{\int - \frac{2}{x} d x}$
69189	Evaluate the Limit	limit as x approaches a of (x^2-a^2)/(x-a)	$lim_{x \to a} \frac{x^{2} - a^{2}}{x - a}$
69190	Find dy/dx	x^(4/3)+y^(4/3)=1	$x^{\frac{4}{3}} + y^{\frac{4}{3}} = 1$
69191	Find the Derivative - d/dZ	Z=A/(y^10)+Be^y	$Z = \frac{A}{y^{10}} + B e^{y}$
69192	Find the Integral	f(x)=4x	$f (x) = 4 x$
69193	Find dy/dx	x^2+2y^2=4	$x^{2} + 2 y^{2} = 4$
69194	Find the Average Value of the Derivative	f(x)=x^3-x^2+2x-1 , [0,2]	$f (x) = x^{3} - x^{2} + 2 x - 1$ , $[0, 2]$
69195	Find dy/dx	y=x^(2/3)	$y = x^{\frac{2}{3}}$
69196	Find the Derivative - d/dt	( natural log of t)^2cos(t)	$\ln^{2} (t) \cos (t)$
69197	Find dy/dx	y=3 square root of sin(x)	$y = 3 \sqrt{\sin (x)}$
69198	Find the Integral	cube root of x^2dx	$\sqrt[3]{x^{2}} d x$
69199	Evaluate the Limit	limit as x approaches 0 from the right of x^2 natural log of x	$lim_{x \to 0^{+}} x^{2} \ln (x)$
69200	Find dy/dx	y = natural log of natural log of x	$y = \ln (\ln (x))$