Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
67501	Evaluate the Integral	integral of (3x^2-2)/((x^3-2x)^5) with respect to x	$\int \frac{(3 x^{2} - 2)}{{(x^{3} - 2 x)}^{5}} d x$
67502	Find the Derivative - d/dx	1/3x^(3/2)	$\frac{1}{3} x^{\frac{3}{2}}$
67503	Find the Tangent Line at (2π,0)	y=sin(sin(x)) , (2pi,0)	$y = \sin (\sin (x))$ , $(2 π, 0)$
67504	Evaluate the Integral	integral from 0 to 4 of (4x-x^2) with respect to x	$\int_{0}^{4} (4 x - x^{2}) d x$
67505	Find the Derivative - d/dx	y=x^3(3x+1)	$y = x^{3} (3 x + 1)$
67506	Find dy/dx	x^2+xy=10	$x^{2} + x y = 10$
67507	Find the Critical Points	f(x)=x square root of x-a	$f (x) = x \sqrt{x - a}$
67508	Find the Derivative - d/dx	y=( square root of x)/2-2/( square root of x)	$y = \frac{\sqrt{x}}{2} - \frac{2}{\sqrt{x}}$
67509	Find the Maximum/Minimum Value	f(x)=x^3-x	$f (x) = x^{3} - x$
67510	Solve the Differential Equation	(dy)/(dx)=y/x	$\frac{d y}{d x} = \frac{y}{x}$
67511	Find dy/dx	x^2+y^2=10	$x^{2} + y^{2} = 10$
67512	Evaluate the Limit	limit as x approaches infinity of x^2e^(-x)	$lim_{x \to \infty} x^{2} e^{- x}$
67513	Find the Derivative - d/dx	y=12^(3x^2+10x-6)+e^(7x)-15x	$y = 12^{3 x^{2} + 10 x - 6} + e^{7 x} - 15 x$
67514	Find dy/dx	ycos(x)=2x^2+5y^2	$y \cos (x) = 2 x^{2} + 5 y^{2}$
67515	Find the Maximum/Minimum Value	f(x)=x^2-x- natural log of x	$f (x) = x^{2} - x - \ln (x)$
67516	Evaluate the Limit	limit as x approaches infinity of (4x^2-3x)/(x^3)	$lim_{x \to \infty} \frac{4 x^{2} - 3 x}{x^{3}}$
67517	Use Logarithmic Differentiation to Find the Derivative	y=(x^4+2)^2(x^3+4)^4	$y = {(x^{4} + 2)}^{2} {(x^{3} + 4)}^{4}$
67518	Find dy/dx	y=x square root of x	$y = x \sqrt{x}$
67519	Evaluate the Integral	integral from negative infinity to 0 of e^x with respect to x	$\int_{- \infty}^{0} e^{x} d x$
67520	Find the Derivative - d/dθ	2sin(theta)	$2 \sin (θ)$
67521	Find dy/dx	natural log of 2x+y=x+1	$\ln (2 x + y) = x + 1$
67522	Find Where Increasing/Decreasing	f(x)=x^(1/3)(x+3)^(2/3)	$f (x) = x^{\frac{1}{3}} {(x + 3)}^{\frac{2}{3}}$
67523	Find the Derivative - d/dx	e^(x^2y)	$e^{x^{2} y}$
67524	Evaluate the Limit	limit as x approaches 0.5 from the left of (2x-1)/(\|2x^3-x^2\|)	$lim_{x \to {0.5}^{-}} \frac{2 x - 1}{\| 2 x^{3} - x^{2} \|}$
67525	Evaluate the Limit	limit as x approaches infinity of (4x^2-3x+1)/(1-3x^2)	$lim_{x \to \infty} \frac{4 x^{2} - 3 x + 1}{1 - 3 x^{2}}$
67526	Find dy/dx	y=2/x	$y = \frac{2}{x}$
67527	Use Logarithmic Differentiation to Find the Derivative	y=(x^4+2)^2(x^5+4)^4	$y = {(x^{4} + 2)}^{2} {(x^{5} + 4)}^{4}$
67528	Find the Center and Radius	2x^2+2y^2+10x=2y+7	$2 x^{2} + 2 y^{2} + 10 x = 2 y + 7$
67529	Find the Derivative - d/dx	x^2+xy+y^2	$x^{2} + x y + y^{2}$
67530	Find dy/dx	x^2+3y^2=3	$x^{2} + 3 y^{2} = 3$
67531	Find dy/dt	y=tan( square root of 7t)	$y = \tan (\sqrt{7 t})$
67532	Evaluate the Integral	integral of ((x^2)/2-2/(x^2)) with respect to x	$\int (\frac{x^{2}}{2} - \frac{2}{x^{2}}) d x$
67533	Evaluate the Integral	integral of (6/( square root of x)+6 square root of x) with respect to x	$\int (\frac{6}{\sqrt{x}} + 6 \sqrt{x}) d x$
67534	Find the Maximum/Minimum Value	f(x)=x	$f (x) = x$
67535	Find dy/dx	4x^2+y^2=9	$4 x^{2} + y^{2} = 9$
67536	Evaluate the Limit	limit as x approaches infinity of (5x^3+2x^2-7)/(x^4+3x)	$lim_{x \to \infty} \frac{5 x^{3} + 2 x^{2} - 7}{x^{4} + 3 x}$
67537	Find dy/dx	y = square root of x^2+11	$y = \sqrt{x^{2} + 11}$
67538	Find the Derivative - d/dx	y=x square root of a+bx	$y = x \sqrt{a + b x}$
67539	Find the Derivative - d/dx	d/(dx)( fifth root of x^2)	$\frac{d}{d x} (\sqrt[5]{x^{2}})$
67540	Find dy/dx	x^2+2xy=y^2	$x^{2} + 2 x y = y^{2}$
67541	Determine if Continuous	f(x)=(x^2-4)/(x-2) if x<2; ax^2-bx+1 if 2<=x<3; 4x-a+b if x>=3	$f (x) = {\begin{cases} \frac{x^{2} - 4}{x - 2} & x < 2 \\ a x^{2} - b x + 1 & 2 \leq x < 3 \\ 4 x - a + b & x \geq 3 \end{cases}$
67542	Find dy/dx	y=x^2cos(x)	$y = x^{2} \cos (x)$
67543	Find dy/dx	y^2=4x	$y^{2} = 4 x$
67544	Find the Maximum/Minimum Value	f(x)=x^3+3x^2	$f (x) = x^{3} + 3 x^{2}$
67545	Find the Maximum/Minimum Value	f(x)=3x^(2/3)-2x	$f (x) = 3 x^{\frac{2}{3}} - 2 x$
67546	Find dy/dx	e^(xy)=6y	$e^{x y} = 6 y$
67547	Evaluate the Integral	integral from negative infinity to infinity of e^(-x^2) with respect to x	$\int_{- \infty}^{\infty} e^{- x^{2}} d x$
67548	Evaluate the Integral	integral from 1 to 8 of ((x^(-1/2))/(1+x^(1/2))) with respect to x	$\int_{1}^{8} (\frac{x^{- \frac{1}{2}}}{1 + x^{\frac{1}{2}}}) d x$
67549	Find dy/dx	x+y=x/y	$x + y = \frac{x}{y}$
67550	Find the Maximum/Minimum Value	f(x)=x(x+3)	$f (x) = x (x + 3)$
67551	Find the Domain and Range	f(x)=-3x+5 if x<1; 3x-1 if x>=1	$f (x) = {\begin{cases} - 3 x + 5 & x < 1 \\ 3 x - 1 & x \geq 1 \end{cases}$
67552	Find Where Increasing/Decreasing	f(x)=1/4x^3-1/2x^2-x+2	$f (x) = \frac{1}{4} x^{3} - \frac{1}{2} x^{2} - x + 2$
67553	Find dy/dx	square root of x+y+xy=21	$\sqrt{x + y} + x y = 21$
67554	Evaluate the Limit	limit as x approaches 4 of ( square root of 2x+1-3)/( square root of x-2- square root of 2)	$lim_{x \to 4} \frac{\sqrt{2 x + 1} - 3}{\sqrt{x - 2} - \sqrt{2}}$
67555	Evaluate the Integral	integral of (3x^2+2x-1) with respect to x	$\int (3 x^{2} + 2 x - 1) d x$
67556	Evaluate the Integral	integral from 0 to 3 of (x^3-6x) with respect to x	$\int_{0}^{3} (x^{3} - 6 x) d x$
67557	Find dy/dx	x^3+y^3=8xy	$x^{3} + y^{3} = 8 x y$
67558	Find dy/dx	9x^2+y^2=9	$9 x^{2} + y^{2} = 9$
67559	Integrate Using u-Substitution	integral of x^2(1-x^3) with respect to x	$\int x^{2} (1 - x^{3}) d x$
67560	Evaluate the Integral	integral from 1 to 4 of (x-1) with respect to x	$\int_{1}^{4} (x - 1) d x$
67561	Use Logarithmic Differentiation to Find the Derivative	y=( square root of x)^(5x)	$y = {(\sqrt{x})}^{5 x}$
67562	Use Logarithmic Differentiation to Find the Derivative	y=x^( natural log of x)	$y = x^{\ln (x)}$
67563	Find the Derivative - d/dx	e^( square root of x^2+1)	$e^{\sqrt{x^{2} + 1}}$
67564	Find the Third Derivative	2x^3-3x^2+6x-1	$2 x^{3} - 3 x^{2} + 6 x - 1$
67565	Find dx/dy	y=x^2e^x	$y = x^{2} e^{x}$
67566	Find dy/dx	sin(x^2y^2)=x	$\sin (x^{2} y^{2}) = x$
67567	Find the Derivative - d/dx	(x+y)	$(x + y)$
67568	Find dy/dx	x^(1/2)+y^(1/2)=16	$x^{\frac{1}{2}} + y^{\frac{1}{2}} = 16$
67569	Find the Antiderivative	square root of 1+x^2	$\sqrt{1 + x^{2}}$
67570	Find dy/dx	y = square root of x^2+8	$y = \sqrt{x^{2} + 8}$
67571	Evaluate the Limit	limit as x approaches infinity of x/(x^2+1)	$lim_{x \to \infty} \frac{x}{x^{2} + 1}$
67572	Evaluate the Limit	limit as x approaches 0 of (5x^n-3x^(n-1)+4x^(n-2))/(2x^n-6x^(n-2))	$lim_{x \to 0} \frac{5 x^{n} - 3 x^{n - 1} + 4 x^{n - 2}}{2 x^{n} - 6 x^{n - 2}}$
67573	Integrate By Parts	integral of x square root of x+3 with respect to x	$\int x \sqrt{x + 3} d x$
67574	Find dy/dx	ycos(x)=x^2+y^2	$y \cos (x) = x^{2} + y^{2}$
67575	Find the Center and Radius	(x^2)/9+(y^2)/4=1	$\frac{x^{2}}{9} + \frac{y^{2}}{4} = 1$
67576	Evaluate the Integral	integral from 1 to 3 of (3x+1) with respect to x	$\int_{1}^{3} (3 x + 1) d x$
67577	Evaluate the Limit	limit as x approaches infinity of 9/(x^2+1)	$lim_{x \to \infty} \frac{9}{x^{2} + 1}$
67578	Evaluate the Limit	limit as x approaches -1 of (2x^2-x-3)/(x^3+2x^2+6x+5)	$lim_{x \to - 1} \frac{2 x^{2} - x - 3}{x^{3} + 2 x^{2} + 6 x + 5}$
67579	Find the Derivative - d/dx	x*e^(-x)	$x \cdot e^{- x}$
67580	Use Logarithmic Differentiation to Find the Derivative	y=x^(cos(x))	$y = x^{\cos (x)}$
67581	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of x^( square root of x)	$lim_{x \to 0^{+}} x^{\sqrt{x}}$
67582	Find the Derivative - d/dθ	2cos(theta)	$2 \cos (θ)$
67583	Find the Derivative - d/dx	xe^(x/2)	$x e^{\frac{x}{2}}$
67584	Evaluate the Integral	integral from -2 to 0 of (5x^2+5x) with respect to x	$\int_{- 2}^{0} (5 x^{2} + 5 x) d x$
67585	Find the Tangent Line at (49,7)	y = square root of x , (49,7)	$y = \sqrt{x}$ , $(49, 7)$
67586	Find Where Increasing/Decreasing	f(x) = square root of 25-x^2	$f (x) = \sqrt{25 - x^{2}}$
67587	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of (1+1/x)^x	$lim_{x \to 0^{+}} {(1 + \frac{1}{x})}^{x}$
67588	Evaluate the Integral	integral from 0 to 0.6 of (x^2)/( square root of 9-25x^2) with respect to x	$\int_{0}^{0.6} \frac{x^{2}}{\sqrt{9 - 25 x^{2}}} d x$
67589	Find the Tangent Line at (81,9)	y = square root of x , (81,9)	$y = \sqrt{x}$ , $(81, 9)$
67590	Find the Antiderivative	f(x)=6x^5-x^4+2x^2-3	$f (x) = 6 x^{5} - x^{4} + 2 x^{2} - 3$
67591	Find the Derivative - d/dθ	2theta	$2 θ$
67592	Evaluate the Integral	integral from 0 to 4 of ( square root of x+3x) with respect to x	$\int_{0}^{4} (\sqrt{x} + 3 x) d x$
67593	Find the Derivative - d/dx	-1/(4x^(3/2))	$- \frac{1}{4 x^{\frac{3}{2}}}$
67594	Evaluate the Limit	limit as x approaches 2 of (x^2-4)/( square root of x- square root of 2)	$lim_{x \to 2} \frac{x^{2} - 4}{\sqrt{x} - \sqrt{2}}$
67595	Find dy/dx	y=x^-4	$y = x^{- 4}$
67596	Evaluate the Integral	integral of (9/( square root of x)+9 square root of x) with respect to x	$\int (\frac{9}{\sqrt{x}} + 9 \sqrt{x}) d x$
67597	Find dy/dt	y=tan( square root of 5t)	$y = \tan (\sqrt{5 t})$
67598	Evaluate the Limit	limit as x approaches infinity of ( cube root of x^3-2x^2+3)/(2x+1)	$lim_{x \to \infty} \frac{\sqrt[3]{x^{3} - 2 x^{2} + 3}}{2 x + 1}$
67599	Evaluate the Integral	integral of 1/2e^(2x) with respect to x	$\int \frac{1}{2} e^{2 x} d x$
67600	Find dy/dx	y=sin(2x)	$y = \sin (2 x)$