Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82701	Find the Derivative - d/dx	x+3 natural log of 5x-4x^2+e^(2x)-pi	$x + 3 \ln (5 x) - 4 x^{2} + e^{2 x} - π$
82702	Find the Derivative - d/dx	d/(dx)(1/3 square root of (x^2+y^2)^3)	$\frac{d}{d x} (\frac{1}{3} \sqrt{{(x^{2} + y^{2})}^{3}})$
82703	Find the Derivative of the Integral	integral of (2x^3+2x)u(x) with respect to x=x^6+2x^4+x^2+C	$\int (2 x^{3} + 2 x) u (x) d x = x^{6} + 2 x^{4} + x^{2} + C$
82704	Find dx/dy	e^(xy)=y-x	$e^{x y} = y - x$
82705	Find the Absolute Max and Min over the Interval	f(x)=12x-x^3 , [0,3]	$f (x) = 12 x - x^{3}$ , $[0, 3]$
82706	Find the Antiderivative	f(x)=x/(1+x)	$f (x) = \frac{x}{1 + x}$
82707	Evaluate the Integral	integral of 5(5^(5x)) with respect to x	$\int 5 (5^{5 x}) d x$
82708	Find the Antiderivative	x/2dx	$\frac{x}{2} d x$
82709	Find the Antiderivative	f(x)=sin(x)+2x	$f (x) = \sin (x) + 2 x$
82710	Evaluate the Integral	integral of (1/(x^2)-sin(x)) with respect to x	$\int (\frac{1}{x^{2}} - \sin (x)) d x$
82711	Find the Derivative - d/dy	y/(y^2+x^2)	$\frac{y}{y^{2} + x^{2}}$
82712	Find the Derivative - d/dx	y=(e^x)/(x+1)	$y = \frac{e^{x}}{x + 1}$
82713	Find dy/dx	x^2=e^(x-y)	$x^{2} = e^{x - y}$
82714	Find the Derivative - d/dx	natural log of x^2(x+1)	$\ln (x^{2} (x + 1))$
82715	Find the Inflection Points	1/6x^6+x^5+5/3x^4	$\frac{1}{6} x^{6} + x^{5} + \frac{5}{3} x^{4}$
82716	Find the Derivative - d/dx	square root of 9xsin(x)	$\sqrt{9 x} \sin (x)$
82717	Find the Derivative - d/dy	tan(y)^2	$\tan^{2} (y)$
82718	Find dy/dx	y=x/(x+y)	$y = \frac{x}{x + y}$
82719	Integrate Using u-Substitution	integral of x square root of x^2+4 with respect to x	$\int x \sqrt{x^{2} + 4} d x$
82720	Evaluate the Integral	integral of (6x^2-8x+6)/(3x^3-6x^2+9x) with respect to x	$\int \frac{6 x^{2} - 8 x + 6}{3 x^{3} - 6 x^{2} + 9 x} d x$
82721	Find dy/dx	y=1/27(9x^2+6)^(3/2)	$y = \frac{1}{27} {(9 x^{2} + 6)}^{\frac{3}{2}}$
82722	Find dy/dx	y=(x^4)/( square root of 3x^3+3)	$y = \frac{x^{4}}{\sqrt{3 x^{3} + 3}}$
82723	Find the Derivative - d/dx	d/(dx)( natural log of x)^2	$\frac{d}{d x} \ln^{2} (x)$
82724	Find the Derivative - d/dx	(2x+5)/3	$\frac{2 x + 5}{3}$
82725	Evaluate the Integral	integral of (16/(x^6)-9/(x^-3)+4/(x^(1/3))) with respect to x	$\int (\frac{16}{x^{6}} - \frac{9}{x^{- 3}} + \frac{4}{x^{\frac{1}{3}}}) d x$
82726	Evaluate the Integral	integral of (-6x^-2+4x^-3+3) with respect to x	$\int (- 6 x^{- 2} + 4 x^{- 3} + 3) d x$
82727	Find the Concavity	1/10x^5-12x^3	$\frac{1}{10} x^{5} - 12 x^{3}$
82728	Find the Concavity	-1/3x^3-7x^2	$- \frac{1}{3} x^{3} - 7 x^{2}$
82729	Find the Derivative - d/dx	sin(x)+e^(-x)+3x	$\sin (x) + e^{- x} + 3 x$
82730	Evaluate the Summation	sum from k=0 to 3 of 6k^2-8k	$\sum_{k = 0}^{3} 6 k^{2} - 8 k$
82731	Evaluate the Limit	limit as x approaches 1/2 of x+10	$lim_{x \to \frac{1}{2}} x + 10$
82732	Find the Derivative - d/dx	(e^x+1)^2	${(e^{x} + 1)}^{2}$
82733	Find dy/dx	xy-4y^2=x-1	$x y - 4 y^{2} = x - 1$
82734	Evaluate the Integral	integral of (x^2+1)/(x^2-x) with respect to x	$\int \frac{x^{2} + 1}{x^{2} - x} d x$
82735	Find the Second Derivative	f(x)=-1/3x^6-1/3x^3-1/3x^-3+1/2x^-4	$f (x) = - \frac{1}{3} x^{6} - \frac{1}{3} x^{3} - \frac{1}{3} x^{- 3} + \frac{1}{2} x^{- 4}$
82736	Find the Domain and Range	f(x)=x+3 if x<=-5; -1 if -5=6	$f (x) = {\begin{cases} x + 3 & x \leq - 5 \\ - 1 & - 5 = 6 \end{cases}$
82737	Find dy/dx	-5y^3-5y+y^2=4x^2	$- 5 y^{3} - 5 y + y^{2} = 4 x^{2}$
82738	Find the Derivative - d/dx	80+4/(x+1)	$80 + \frac{4}{x + 1}$
82739	Find dy/dx	y=((5x)/(6-5x^3))^3	$y = {(\frac{5 x}{6 - 5 x^{3}})}^{3}$
82740	Find the Antiderivative	cos(x)*e^(sin(x))	$\cos (x) \cdot e^{\sin (x)}$
82741	Find the Antiderivative	(x-1)e^x	$(x - 1) e^{x}$
82742	Find dy/dx	5^(x+y)=5^x+5^y	$5^{x + y} = 5^{x} + 5^{y}$
82743	Find the Derivative - d/dx	fourth root of 8x^2	$\sqrt[4]{8 x^{2}}$
82744	Evaluate the Integral	integral of (2x-3)^3x with respect to x	$\int {(2 x - 3)}^{3} x d x$
82745	Find dy/dx	y=2tan(x)	$y = 2 \tan (x)$
82746	Integrate Using u-Substitution	integral of x cube root of 3-2x with respect to x	$\int x \sqrt[3]{3 - 2 x} d x$
82747	Find dy/dx	e^(x+y)=xy	$e^{x + y} = x y$
82748	Evaluate the Limit	limit as x approaches infinity of ce^(-x)	$lim_{x \to \infty} c e^{- x}$
82749	Find the Antiderivative	(x+1)(x+2)	$(x + 1) (x + 2)$
82750	Find the Maximum/Minimum Value	f(x)=x^3+1	$f (x) = x^{3} + 1$
82751	Evaluate the Integral	integral from 2 to 3 of (t^2-9)(4-t^2) with respect to t	$\int_{2}^{3} (t^{2} - 9) (4 - t^{2}) d t$
82752	Find the Maximum/Minimum Value	f(x)=10x^2+x	$f (x) = 10 x^{2} + x$
82753	Evaluate the Integral	integral of 1/((5x-3)(3-4x)) with respect to x	$\int \frac{1}{(5 x - 3) (3 - 4 x)} d x$
82754	Find the Integral	x/(e^x)	$\frac{x}{e^{x}}$
82755	Find dy/dx	y=cos(xy)	$y = \cos (x y)$
82756	Find the Derivative - d/dx	y=(1-x)^2sinh(2x)	$y = {(1 - x)}^{2} \sinh (2 x)$
82757	Use Logarithmic Differentiation to Find the Derivative	j(x)=(sin(2x)^5)/(cos(2x)^5)	$j (x) = \frac{\sin^{5} (2 x)}{\cos^{5} (2 x)}$
82758	Find the Domain and Range	k(x)=x+4 if x<-1; 5 if -1=2	$k (x) = {\begin{cases} x + 4 & x < - 1 \\ 5 & - 1 = 2 \end{cases}$
82759	Find the Antiderivative	f(x)=4/(x^5)-(1-2x)^3	$f (x) = \frac{4}{x^{5}} - {(1 - 2 x)}^{3}$
82760	Evaluate the Integral	integral from 1 to 4 of ( square root of y-y)/(y^2) with respect to y	$\int_{1}^{4} \frac{\sqrt{y} - y}{y^{2}} d y$
82761	Evaluate the Integral	integral of ((x-8)/(x+12)) with respect to x	$\int (\frac{x - 8}{x + 12}) d x$
82762	Find the Concavity	1/6x^4+5x^3+50x^2	$\frac{1}{6} x^{4} + 5 x^{3} + 50 x^{2}$
82763	Find the Antiderivative	square root of 2cos(x)	$\sqrt{2} \cos (x)$
82764	Find the Derivative - d/dx	cube root of x^3	$\sqrt[3]{x^{3}}$
82765	Find the Derivative - d/dx	(x^2+1)^(2x)	${(x^{2} + 1)}^{2 x}$
82766	Find dy/dx	y=(x^3+4+5x^2)sin(x)	$y = (x^{3} + 4 + 5 x^{2}) \sin (x)$
82767	Find the Antiderivative	e^x(3+e^(-x))	$e^{x} (3 + e^{- x})$
82768	Find the Derivative - d/dx	(2(x^2-9))/(x^2-4)	$\frac{2 (x^{2} - 9)}{x^{2} - 4}$
82769	Evaluate the Integral	integral of (-6+5x+x^-3) with respect to x	$\int (- 6 + 5 x + x^{- 3}) d x$
82770	Find the Integral	(x^2+1)^2	${(x^{2} + 1)}^{2}$
82771	Find the Inflection Points	f(x)=x^2\|x\|	$f (x) = x^{2} \| x \|$
82772	Find the Derivative - d/dx	d/(dx)(x+5)	$\frac{d}{d x} (x + 5)$
82773	Find the Maximum/Minimum Value	f(x)=2/5x^5+5x^4+16x^3-15	$f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15$
82774	Find dx/dy	y=x square root of 1-x^2	$y = x \sqrt{1 - x^{2}}$
82775	Find dy/dx	y=x-xsin(x)	$y = x - x \sin (x)$
82776	Find the Antiderivative	g(x)=(x^2+3x-5)/(x^4)	$g (x) = \frac{x^{2} + 3 x - 5}{x^{4}}$
82777	Find dy/dx	-4y^2+3-3x^2-4x=0	$- 4 y^{2} + 3 - 3 x^{2} - 4 x = 0$
82778	Evaluate the Integral	integral of x^4-3x^3+6x^2-7 with respect to x	$\int x^{4} - 3 x^{3} + 6 x^{2} - 7 d x$
82779	Find the Antiderivative	x^(1/3)+x square root of x-2	$x^{\frac{1}{3}} + x \sqrt{x} - 2$
82780	Find the Domain and Range	f(x)=x+1 if x<=-5; -3 if -5=6	$f (x) = {\begin{cases} x + 1 & x \leq - 5 \\ - 3 & - 5 = 6 \end{cases}$
82781	Find Where Increasing/Decreasing	f(x)=2 log base 2 of x-2	$f (x) = 2 \log_{2} (x - 2)$
82782	Find Where Increasing/Decreasing	f(x)=x^(2/3)(x^2-4)	$f (x) = x^{\frac{2}{3}} (x^{2} - 4)$
82783	Find dy/dx	y=(2x^3+2)^4cos(x)^3	$y = {(2 x^{3} + 2)}^{4} \cos^{3} (x)$
82784	Find the Derivative - d/dx	natural log of \|1-x\|	$\ln (\| 1 - x \|)$
82785	Integrate By Parts	integral from 0 to 1 of arctan(2x) with respect to x	$\int_{0}^{1} \arctan (2 x) d x$
82786	Evaluate the Limit	limit as x approaches 0 of square root of -2x^3-5x^2+2x+2	$lim_{x \to 0} \sqrt{- 2 x^{3} - 5 x^{2} + 2 x + 2}$
82787	Find the Derivative - d/dx	sin(pi/2x)	$\sin (\frac{π}{2} x)$
82788	Find the Antiderivative	(e^x)/(e^x+3)	$\frac{e^{x}}{e^{x} + 3}$
82789	Find Where Increasing/Decreasing	xe^(-x)	$x e^{- x}$
82790	Find the Derivative - d/dx	1/(2(x+1)^(1/2))	$\frac{1}{2 {(x + 1)}^{\frac{1}{2}}}$
82791	Evaluate the Summation	5 sum from i=1 to 5 of 9i-3i^2	$5 \sum_{i = 1}^{5} 9 i - 3 i^{2}$
82792	Find the Derivative - d/dt	1/2t^2+1	$\frac{1}{2} t^{2} + 1$
82793	Find the Antiderivative	3(x+1)^2	$3 {(x + 1)}^{2}$
82794	Find the Derivative - d/dx	x+pisec(x)	$x + π \sec (x)$
82795	Find the Second Derivative	f(x)=((1-x^2)/(1-x))^2	$f (x) = {(\frac{1 - x^{2}}{1 - x})}^{2}$
82796	Find the Derivative - d/dx	y=5x-4 square root of x	$y = 5 x - 4 \sqrt{x}$
82797	Find dy/dx	-y-2-2x^2=y^3	$- y - 2 - 2 x^{2} = y^{3}$
82798	Find Where Increasing/Decreasing	f(x)=4x^3	$f (x) = 4 x^{3}$
82799	Find the Derivative - d/dx	-(x+1)sin((x^2)/2)	$- (x + 1) \sin (\frac{x^{2}}{2})$
82800	Find the Derivative - d/dy	natural log of square root of x^2+y^2	$\ln (\sqrt{x^{2} + y^{2}})$