Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
84601	Find the Derivative - d/dx	y=2^(5x)*3^(4x^2)	$y = 2^{5 x} \cdot 3^{4 x^{2}}$
84602	Find the Derivative - d/dx	1-tan(x)^2	$1 - \tan^{2} (x)$
84603	Find the Derivative - d/dx	y=sin(x^2+3x)^4	$y = \sin^{4} (x^{2} + 3 x)$
84604	Find dx/dy	y=x^(2/3)	$y = x^{\frac{2}{3}}$
84605	Find dy/dx	y=(-6+x-6x^2)(-9-9x)	$y = (- 6 + x - 6 x^{2}) (- 9 - 9 x)$
84606	Evaluate the Integral	4 integral from 0 to 1 of x^3 square root of 1-x^2 with respect to x	$4 \int_{0}^{1} x^{3} \sqrt{1 - x^{2}} d x$
84607	Find dy/dx	y=( square root of 4+6x^3)/(cos(x)^3)	$y = \frac{\sqrt{4 + 6 x^{3}}}{\cos^{3} (x)}$
84608	Find the Derivative - d/dx	xy^2-sin(x+y)+y	$x y^{2} - \sin (x + y) + y$
84609	Find the Maximum/Minimum Value	y=4-6x+x^3	$y = 4 - 6 x + x^{3}$
84610	Find the Critical Points	y=4-6x+x^3	$y = 4 - 6 x + x^{3}$
84611	Find the Antiderivative	1/(sin(2x))	$\frac{1}{\sin (2 x)}$
84612	Find the Antiderivative	(x^2+x+1)/(x+2)	$\frac{x^{2} + x + 1}{x + 2}$
84613	Find the Antiderivative	x^2+3/x-2 square root of x	$x^{2} + \frac{3}{x} - 2 \sqrt{x}$
84614	Find the Derivative - d/dx	-tan(10x^2)	$- \tan (10 x^{2})$
84615	Find the Derivative - d/dx	y=e^(x^3+8x^2)	$y = e^{x^{3} + 8 x^{2}}$
84616	Find the Derivative - d/dx	arctan( square root of x-6)	$\arctan (\sqrt{x - 6})$
84617	Evaluate the Limit	limit as x approaches pi from the right of ( square root of x)/(csc(x))	$lim_{x \to π^{+}} \frac{\sqrt{x}}{\csc (x)}$
84618	Find the Antiderivative	(5x+1)e^x	$(5 x + 1) e^{x}$
84619	Find Where Increasing/Decreasing	f(x)=x^(5/3)	$f (x) = x^{\frac{5}{3}}$
84620	Evaluate the Integral	integral from 1 to e of ( natural log of x)/(11x^2) with respect to x	$\int_{1}^{e} \frac{\ln (x)}{11 x^{2}} d x$
84621	Find the Antiderivative	(e^(-x))/(1+e^(-x))	$\frac{e^{- x}}{1 + e^{- x}}$
84622	Evaluate the Limit	limit as x approaches 0 of (7-7cos(x))/x	$lim_{x \to 0} \frac{7 - 7 \cos (x)}{x}$
84623	Evaluate the Integral	integral from 0 to 2 of (x^2-2)/(x+1) with respect to x	$\int_{0}^{2} \frac{x^{2} - 2}{x + 1} d x$
84624	Find Where Increasing/Decreasing	y=-4x^3-5x^2	$y = - 4 x^{3} - 5 x^{2}$
84625	Find the Derivative - d/dx	2csc(x)^3	$2 \csc^{3} (x)$
84626	Evaluate the Integral	integral of (x-2)^2+1 with respect to x	$\int {(x - 2)}^{2} + 1 d x$
84627	Find the Derivative - d/dx	d/(dx)(f(x)g(x))	$\frac{d}{d x} (f (x) g (x))$
84628	Evaluate the Integral	integral from pi/6 to pi/2 of 7cot(x)^2 with respect to x	$\int_{\frac{π}{6}}^{\frac{π}{2}} 7 \cot^{2} (x) d x$
84629	Find dy/dx	5-2x^2+y^3+y^2=x	$5 - 2 x^{2} + y^{3} + y^{2} = x$
84630	Find the Derivative - d/dy	1/( square root of y)	$\frac{1}{\sqrt{y}}$
84631	Evaluate the Limit	limit as x approaches 200 from the left of (3-0.015x)^2	$lim_{x \to 200^{-}} {(3 - 0.015 x)}^{2}$
84632	Find the Antiderivative	natural log of (x)^3	$\ln ({(x)}^{3})$
84633	Find the Derivative - d/dx	d/(dx)(6x)/(e^x)	$\frac{d}{d x} \cdot \frac{6 x}{e^{x}}$
84634	Find the Antiderivative	f(x)=(4-5x)^4	$f (x) = {(4 - 5 x)}^{4}$
84635	Evaluate the Limit	limit as x approaches -3 of (x^3+5)/(2-3x)	$lim_{x \to - 3} \frac{x^{3} + 5}{2 - 3 x}$
84636	Evaluate the Integral	integral from -1 to 4 of [3y-(y^2-4)] with respect to y	$\int_{- 1}^{4} [3 y - (y^{2} - 4)] d y$
84637	Find Where Increasing/Decreasing	f(x)=2 log base 3 of x-2	$f (x) = 2 \log_{3} (x - 2)$
84638	Evaluate the Integral	integral of y^2 cube root of y with respect to y	$\int y^{2} \sqrt[3]{y} d y$
84639	Find the Derivative - d/dx	e^(-1/2x^2)	$e^{- \frac{1}{2} x^{2}}$
84640	Find dy/dx	y = cube root of x^2+5	$y = \sqrt[3]{x^{2} + 5}$
84641	Evaluate the Limit	limit as x approaches 1 of (1-y root of x)/(1-z root of x)	$lim_{x \to 1} \frac{1 - \sqrt[y]{x}}{1 - \sqrt[z]{x}}$
84642	Find the Derivative - d/dx	y=x+4 square root of x+2	$y = x + 4 \sqrt{x + 2}$
84643	Find dy/dx	y*2^y=x	$y \cdot 2^{y} = x$
84644	Find the Inflection Points	1/10x^5-3x^3	$\frac{1}{10} x^{5} - 3 x^{3}$
84645	Evaluate the Integral	integral from -3 to 4 of (y-(y^2-12)) with respect to y	$\int_{- 3}^{4} (y - (y^{2} - 12)) d y$
84646	Find the Antiderivative	6x-9+3x^5	$6 x - 9 + 3 x^{5}$
84647	Integrate Using u-Substitution	integral of cos(7x) with respect to x , u=7x	$\int \cos (7 x) d x$ , $u = 7 x$
84648	Find dy/dx	y=arctan( square root of x-4)	$y = \arctan (\sqrt{x - 4})$
84649	Find the Integral	(2x-1)(3x+1)dx	$(2 x - 1) (3 x + 1) d x$
84650	Find the Derivative - d/dx	sin(2x-pi/3)	$\sin (2 x - \frac{π}{3})$
84651	Find the Tangent Line at (6,1/2)	f(x)=3/x at (6,1/2)	$f (x) = \frac{3}{x}$ at $(6, \frac{1}{2})$
84652	Evaluate the Limit	limit as x approaches infinity of (5x^3-2x^2-1)/(x^3-x+1)	$lim_{x \to \infty} \frac{5 x^{3} - 2 x^{2} - 1}{x^{3} - x + 1}$
84653	Find the Concavity	3/20x^5-2x^4+8x^3	$\frac{3}{20} x^{5} - 2 x^{4} + 8 x^{3}$
84654	Find Where Increasing/Decreasing	x^4-12x^3+36x^2	$x^{4} - 12 x^{3} + 36 x^{2}$
84655	Find the Maximum/Minimum Value	x^2 natural log of x	$x^{2} \ln (x)$
84656	Evaluate the Integral	integral of (3x^3)/(x^4) with respect to x	$\int \frac{3 x^{3}}{x^{4}} d x$
84657	Integrate Using u-Substitution	integral from -1 to 1 of x(x^2+1)^3 with respect to x	$\int_{- 1}^{1} x {(x^{2} + 1)}^{3} d x$
84658	Integrate By Parts	integral of xsin(6x) with respect to x	$\int x \sin (6 x) d x$
84659	Find the Derivative - d/dx	y=cos(x-1)	$y = \cos (x - 1)$
84660	Evaluate the Limit	limit as x approaches c of square root of 12*3/4	$lim_{x \to c} \sqrt{12 \cdot \frac{3}{4}}$
84661	Evaluate the Limit	limit as x approaches 0 of (3\|x\|)/(x^2)	$lim_{x \to 0} \frac{3 \| x \|}{x^{2}}$
84662	Evaluate the Integral	integral from -8 to 4 of 14/((9-2x)^(3/2)) with respect to x	$\int_{- 8}^{4} \frac{14}{{(9 - 2 x)}^{\frac{3}{2}}} d x$
84663	Evaluate the Integral	integral of (x-3)(4x-1) with respect to x	$\int (x - 3) (4 x - 1) d x$
84664	Find the Antiderivative	f(x)=1/(sin(4x-pi/3)^2)	$f (x) = \frac{1}{\sin^{2} (4 x - \frac{π}{3})}$
84665	Find the Derivative - d/dx	5e^x+5e^(-x)	$5 e^{x} + 5 e^{- x}$
84666	Find the Maximum/Minimum Value	x^(2/3)	$x^{\frac{2}{3}}$
84667	Find the Derivative - d/dD(x)	D_x((2x+5)/(x^2-1))	$D_{x} (\frac{2 x + 5}{x^{2} - 1})$
84668	Evaluate the Limit	limit as x approaches 15 of 2/( square root of x+5)	$lim_{x \to 15} \frac{2}{\sqrt{x + 5}}$
84669	Find the Derivative - d/dA	sin(2A)	$\sin (2 A)$
84670	Find the Derivative - d/dx	2/(-x^2-9)	$\frac{2}{- x^{2} - 9}$
84671	Evaluate the Limit	limit as x approaches natural log of 10 of e^x+2	$lim_{x \to \ln (10)} e^{x} + 2$
84672	Find the Derivative - d/dx	(3x^2-1)/3	$\frac{3 x^{2} - 1}{3}$
84673	Evaluate the Integral	integral from 1 to x^2+1 of (2t+2)/( square root of t+1) with respect to t	$\int_{1}^{x^{2} + 1} \frac{2 t + 2}{\sqrt{t + 1}} d t$
84674	Find the Maximum/Minimum Value	f(x)=-5sin(1/3x)-15	$f (x) = - 5 \sin (\frac{1}{3} x) - 15$
84675	Find the Antiderivative	f(x)=6/((4-3x)^2)	$f (x) = \frac{6}{{(4 - 3 x)}^{2}}$
84676	Evaluate the Integral	integral of (2x^4+2x^2-5x^-3) with respect to x	$\int (2 x^{4} + 2 x^{2} - 5 x^{- 3}) d x$
84677	Evaluate the Integral	integral of (3x^2)/((3x^3-2)^(2/3)) with respect to x	$\int \frac{3 x^{2}}{{(3 x^{3} - 2)}^{\frac{2}{3}}} d x$
84678	Find the Antiderivative	e^(-x)dx	$e^{- x} d x$
84679	Find the Derivative - d/dt	Differentiate y=4 log base 3 of t	Differentiate $y = 4 \log_{3} (t)$
84680	Find the Antiderivative	1/x+1	$\frac{1}{x} + 1$
84681	Find the Antiderivative	x*e^(3x)	$x \cdot e^{3 x}$
84682	Find Where Increasing/Decreasing	f(x)=x square root of 4-x	$f (x) = x \sqrt{4 - x}$
84683	Find the Antiderivative	(x+3)e^(-2x)	$(x + 3) e^{- 2 x}$
84684	Find the Derivative - d/dx	sin(x^3-x)	$\sin (x^{3} - x)$
84685	Find the Antiderivative	1/(cos(x)^2)-1/(sin(x)^2)	$\frac{1}{\cos^{2} (x)} - \frac{1}{\sin^{2} (x)}$
84686	Evaluate the Integral	integral from 0 to 1 of 1/(x^2+x+1) with respect to x	$\int_{0}^{1} \frac{1}{x^{2} + x + 1} d x$
84687	Find dy/dx	y = square root of 5x^2+3x	$y = \sqrt{5 x^{2} + 3 x}$
84688	Evaluate the Limit	limit as x approaches infinity of 2/(x^2)	$lim_{x \to \infty} \frac{2}{x^{2}}$
84689	Find the Antiderivative	f(x)=-1/(x^2)+x	$f (x) = - \frac{1}{x^{2}} + x$
84690	Find the Antiderivative	(cos(x))/(1+sin(x))	$\frac{\cos (x)}{1 + \sin (x)}$
84691	Evaluate Using L'Hospital's Rule	limit as x approaches 2 of ( square root of 2+x-2)/(x-2)	$lim_{x \to 2} \frac{\sqrt{2 + x} - 2}{x - 2}$
84692	Find the Antiderivative	f(x)=1/(x^-3)+5xy- square root of x	$f (x) = \frac{1}{x^{- 3}} + 5 x y - \sqrt{x}$
84693	Evaluate the Integral	integral of 9(sin(2x))/(sin(x)) with respect to x	$\int 9 \frac{\sin (2 x)}{\sin (x)} d x$
84694	Evaluate the Integral	integral of 1/(by^2+b^3) with respect to y	$\int \frac{1}{b y^{2} + b^{3}} d y$
84695	Evaluate the Limit	limit as x approaches infinity of ((1+x)/(2+x))^((1- square root of x)/(1-x))	$lim_{x \to \infty} {(\frac{1 + x}{2 + x})}^{\frac{1 - \sqrt{x}}{1 - x}}$
84696	Find the Maximum/Minimum Value	y=x^4	$y = x^{4}$
84697	Integrate Using u-Substitution	integral of (e^x+e^(-x))/(e^x-e^(-x)) with respect to x	$\int \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} d x$
84698	Evaluate the Limit	limit as x approaches 0 of (2e^(2x)-2)/(x^2+x)	$lim_{x \to 0} \frac{2 e^{2 x} - 2}{x^{2} + x}$
84699	Evaluate the Limit	limit as x approaches 2 from the right of 1/(x-2)-4/( natural log of 2x-3)	$lim_{x \to 2^{+}} \frac{1}{x - 2} - \frac{4}{\ln (2 x - 3)}$
84700	Find the Derivative - d/dx	x^3+x^2+3	$x^{3} + x^{2} + 3$