Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67601	Find dy/dx	e^(xy)=2y	$e^{x y} = 2 y$
67602	Evaluate the Limit	limit as x approaches 1/2 of ( square root of 4x^2+3-2)/(2x-1)	$lim_{x \to \frac{1}{2}} \frac{\sqrt{4 x^{2} + 3} - 2}{2 x - 1}$
67603	Evaluate the Limit	limit as x approaches infinity of ((x-1)^2-(x+1)^2)/(7x-5)	$lim_{x \to \infty} \frac{{(x - 1)}^{2} - {(x + 1)}^{2}}{7 x - 5}$
67604	Find the Derivative - d/dx	x/( square root of x^2+y^2)	$\frac{x}{\sqrt{x^{2} + y^{2}}}$
67605	Find dy/dx	ycos(x)=2x^2+3y^2	$y \cos (x) = 2 x^{2} + 3 y^{2}$
67606	Find dy/dx	y=x^(x^2)	$y = x^{x^{2}}$
67607	Find dx/dy	x^2+y^2=a^2	$x^{2} + y^{2} = a^{2}$
67608	Evaluate the Limit	limit as x approaches -2 of x^5+x^3+x	$lim_{x \to - 2} x^{5} + x^{3} + x$
67609	Find the Center and Radius	(x-1)^2+(y^2)/25=1	${(x - 1)}^{2} + \frac{y^{2}}{25} = 1$
67610	Evaluate the Limit	limit as x approaches 0 of (cos(x)+3e^x)/(2e^x)	$lim_{x \to 0} \frac{\cos (x) + 3 e^{x}}{2 e^{x}}$
67611	Evaluate the Limit	limit as x approaches infinity of (e^x)/x	$lim_{x \to \infty} \frac{e^{x}}{x}$
67612	Evaluate the Limit	limit as x approaches 0 from the right of (\|x\|)/x	$lim_{x \to 0^{+}} \frac{\| x \|}{x}$
67613	Find dy/dx	y=(e^x)/x	$y = \frac{e^{x}}{x}$
67614	Evaluate the Limit	limit as x approaches infinity of ( natural log of 3x)/( square root of 3x)	$lim_{x \to \infty} \frac{\ln (3 x)}{\sqrt{3 x}}$
67615	Evaluate the Limit	limit as x approaches 4 of (x^2-8)(4x-8)	$lim_{x \to 4} (x^{2} - 8) (4 x - 8)$
67616	Find the Derivative - d/dt	y=8t^-4	$y = 8 t^{- 4}$
67617	Find dy/dx	xe^y-10x+3y=0	$x e^{y} - 10 x + 3 y = 0$
67618	Evaluate the Integral	integral from 0 to 3 of (x^2+1) with respect to x	$\int_{0}^{3} (x^{2} + 1) d x$
67619	Find dx/dy	x^(2/3)+y^(2/3)=4	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$
67620	Find dy/dx	square root of x+y=x^4+y^4	$\sqrt{x + y} = x^{4} + y^{4}$
67621	Find the Derivative - d/dx	-1/((1+x)^2)	$- \frac{1}{{(1 + x)}^{2}}$
67622	Find dy/dx	xy+y^2=1	$x y + y^{2} = 1$
67623	Evaluate the Integral	integral from -3 to 3 of (9-x^2) with respect to x	$\int_{- 3}^{3} (9 - x^{2}) d x$
67624	Find dy/dx	y=e^(x/2)	$y = e^{\frac{x}{2}}$
67625	Find dA/dr	A=pir^2	$A = π r^{2}$
67626	Evaluate the Integral	integral of (e^x+e^(-x))^2 with respect to x	$\int {(e^{x} + e^{- x})}^{2} d x$
67627	Find dy/dx	y=5x^2e^(3x)	$y = 5 x^{2} e^{3 x}$
67628	Find the Domain and Range	f(x)=x^2 if x<=0; 1/x if x>0	$f (x) = {\begin{cases} x^{2} & x \leq 0 \\ \frac{1}{x} & x > 0 \end{cases}$
67629	Integrate Using u-Substitution	integral of x square root of x+2 with respect to x	$\int x \sqrt{x + 2} d x$
67630	Find dy/dx	tan(4x+y)=4x	$\tan (4 x + y) = 4 x$
67631	Find dy/dx	y = natural log of x	$y = \ln (x)$
67632	Find dy/dx	x^2+7y^2=7	$x^{2} + 7 y^{2} = 7$
67633	Find the Derivative - d/dx	tan(x)-cot(x)	$\tan (x) - \cot (x)$
67634	Find the Derivative - d/dx	f(-1)	$f (- 1)$
67635	Find the Domain and Range	g(x)=-x if x<-5; 3 if x>-5	$g (x) = {\begin{cases} - x & x < - 5 \\ 3 & x > - 5 \end{cases}$
67636	Evaluate the Integral	integral from 1 to 4 of (2x+1) with respect to x	$\int_{1}^{4} (2 x + 1) d x$
67637	Find the Derivative - d/dx	y=1/2x^2 square root of 16-x^2	$y = \frac{1}{2} x^{2} \sqrt{16 - x^{2}}$
67638	Find the Antiderivative	(x+1)^2	${(x + 1)}^{2}$
67639	Integrate Using Trig Substitution	integral of (x^2)/( square root of 4-x^2) with respect to x	$\int \frac{x^{2}}{\sqrt{4 - x^{2}}} d x$
67640	Find the Antiderivative	square root of 2	$\sqrt{2}$
67641	Evaluate the Integral	integral of (x^2)/( cube root of 1+2x) with respect to x	$\int \frac{x^{2}}{\sqrt[3]{1 + 2 x}} d x$
67642	Find dy/dx	2xy+y^2=x+y	$2 x y + y^{2} = x + y$
67643	Find the Antiderivative	h(x)=(6x^2+2)/( square root of x^3+x+1)	$h (x) = \frac{6 x^{2} + 2}{\sqrt{x^{3} + x + 1}}$
67644	Find dy/dx	y=x^(e^x)	$y = x^{e^{x}}$
67645	Evaluate the Integral	integral from 0 to 49 of 1/( cube root of (27+2x)^2) with respect to x	$\int_{0}^{49} \frac{1}{\sqrt[3]{{(27 + 2 x)}^{2}}} d x$
67646	Find the Derivative - d/dx	x/(y^2)	$\frac{x}{y^{2}}$
67647	Find the Maximum/Minimum Value	f(x)=x+32/(x^2)	$f (x) = x + \frac{32}{x^{2}}$
67648	Find the Antiderivative	1/( cube root of x)	$\frac{1}{\sqrt[3]{x}}$
67649	Find the Derivative - d/dx	e^xcosh(x)	$e^{x} \cosh (x)$
67650	Find the Tangent Line at (π,-1)	y=(1+sin(x))/(cos(x)) , (pi,-1)	$y = \frac{1 + \sin (x)}{\cos (x)}$ , $(π, - 1)$
67651	Find Where Increasing/Decreasing	f(x)=1/25x^3-1/5x^2-x+5	$f (x) = \frac{1}{25} x^{3} - \frac{1}{5} x^{2} - x + 5$
67652	Integrate By Parts	integral of x^3e^(2x) with respect to x	$\int x^{3} e^{2 x} d x$
67653	Evaluate the Limit	limit as x approaches infinity of x/(e^x)	$lim_{x \to \infty} \frac{x}{e^{x}}$
67654	Find the Derivative - d/dx	y=sin(2x^3+5x)	$y = \sin (2 x^{3} + 5 x)$
67655	Determine if Continuous	f(x)=6 if x<-4; -10+x^2 if -4<=x<4; 2x-2 if x>=4	$f (x) = {\begin{cases} 6 & x < - 4 \\ - 10 + x^{2} & - 4 \leq x < 4 \\ 2 x - 2 & x \geq 4 \end{cases}$
67656	Find dy/dx	x^2+2xy-y^2+x=2	$x^{2} + 2 x y - y^{2} + x = 2$
67657	Find the Derivative - d/dy	(x+y)^2	${(x + y)}^{2}$
67658	Find dy/dx	3y^2=(2x-5)/(2x+5)	$3 y^{2} = \frac{2 x - 5}{2 x + 5}$
67659	Find Where Increasing/Decreasing	f(x)=(11-x)(x+1)^2	$f (x) = (11 - x) {(x + 1)}^{2}$
67660	Evaluate the Integral	integral from 1 to 4 of (1/(x^2)-8/(x^3)) with respect to x	$\int_{1}^{4} (\frac{1}{x^{2}} - \frac{8}{x^{3}}) d x$
67661	Use Logarithmic Differentiation to Find the Derivative	y=( square root of x)^(3x)	$y = {(\sqrt{x})}^{3 x}$
67662	Find dy/dx	x^2-xy+y^2=1	$x^{2} - x y + y^{2} = 1$
67663	Find the Antiderivative	pi	$π$
67664	Find the Derivative - d/dθ	thetacos(theta)	$θ \cos (θ)$
67665	Find the Linearization at a=9	f(x) = square root of x , a=9	$f (x) = \sqrt{x}$ , $a = 9$
67666	Evaluate the Limit	limit as x approaches infinity of (x/(x+1))^x	$lim_{x \to \infty} {(\frac{x}{x + 1})}^{x}$
67667	Find Where Increasing/Decreasing	f(x)=xe^x	$f (x) = x e^{x}$
67668	Find dy/dx	y = cube root of x^2	$y = \sqrt[3]{x^{2}}$
67669	Find the Second Derivative	(sin(x)+cos(x))	$(\sin (x) + \cos (x))$
67670	Find the Derivative - d/dx	Y=(4x^(3/2)-2x^(1/2))^3	$Y = {(4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})}^{3}$
67671	Integrate By Parts	integral of xe^(4x) with respect to x	$\int x e^{4 x} d x$
67672	Evaluate the Integral	integral from 1 to infinity of ( natural log of x)/x with respect to x	$\int_{1}^{\infty} \frac{\ln (x)}{x} d x$
67673	Find the Derivative - d/dx	(x^2-1)	$(x^{2} - 1)$
67674	Find dy/dx	y=4^x	$y = 4^{x}$
67675	Find dy/dx	x^3+y^3-9xy=0	$x^{3} + y^{3} - 9 x y = 0$
67676	Integrate Using u-Substitution	integral of e^(-x) with respect to x	$\int e^{- x} d x$
67677	Find the Derivative - d/dy	x/(y^2)	$\frac{x}{y^{2}}$
67678	Find the Derivative - d/dx	(x-y)/(x+y)	$\frac{x - y}{x + y}$
67679	Find dy/dx	y=sin(x)^x	$y = {\sin (x)}^{x}$
67680	Find dy/dx	x^2+y^2=x+y	$x^{2} + y^{2} = x + y$
67681	Find the Tangent Line at (π,0)	y=sin(sin(x)) , (pi,0)	$y = \sin (\sin (x))$ , $(π, 0)$
67682	Find dy/dx	y^2=10x	$y^{2} = 10 x$
67683	Find dy/dx	2x^3=2y^2+5	$2 x^{3} = 2 y^{2} + 5$
67684	Evaluate the Limit	limit as x approaches 2 of (2x+1)/( log base 2 of x)	$lim_{x \to 2} \frac{2 x + 1}{\log_{2} (x)}$
67685	Find the Derivative - d/dx	y=sec(4x)	$y = \sec (4 x)$
67686	Find dy/dx	3y^2=(4x-5)/(4x+5)	$3 y^{2} = \frac{4 x - 5}{4 x + 5}$
67687	Find the Maximum/Minimum Value	f(x)=3x^5-5x^3	$f (x) = 3 x^{5} - 5 x^{3}$
67688	Evaluate the Limit	limit as x approaches infinity of (1-x)/(1+x)	$lim_{x \to \infty} \frac{1 - x}{1 + x}$
67689	Find dy/dx	2x^3y^4 = square root of x-y	$2 x^{3} y^{4} = \sqrt{x - y}$
67690	Find the Derivative - d/dy	ycos(xy)	$y \cos (x y)$
67691	Find dy/dx	(dy)/(dx)=-x/y	$\frac{d y}{d x} = - \frac{x}{y}$
67692	Find the Derivative - d/dx	(x^3+2)/3	$\frac{x^{3} + 2}{3}$
67693	Find dy/dx	y=5x	$y = 5 x$
67694	Evaluate the Integral	integral of ((1+sin(2x))/(cos(2x))) with respect to x	$\int (\frac{1 + \sin (2 x)}{\cos (2 x)}) d x$
67695	Find dy/dx	sin(x)=x(1+tan(y))	$\sin (x) = x (1 + \tan (y))$
67696	Find the Derivative - d/dx	x square root of y	$x \sqrt{y}$
67697	Find dy/dx	y=x^-8	$y = x^{- 8}$
67698	Find the Derivative - d/dx	(x+1)^3-x^3	${(x + 1)}^{3} - x^{3}$
67699	Find the Slope	-1/4	$- \frac{1}{4}$
67700	Find the Maximum/Minimum Value	y=\|x\|	$y = \| x \|$