Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82501	Find dy/dx	-xy=y-3+2x	$- x y = y - 3 + 2 x$
82502	Find the Derivative - d/dx	y=x- natural log of x	$y = x - \ln (x)$
82503	Find the Skew	3 , 4 , 5 , 12	$3$ , $4$ , $5$ , $12$
82504	Find the Critical Points	f(x) = cube root of x^2+2x	$f (x) = \sqrt[3]{x^{2}} + 2 x$
82505	Find the Antiderivative	e^((-x)/2)	$e^{\frac{- x}{2}}$
82506	Evaluate the Integral	integral from 0 to 1 of (ax^2+b) with respect to x	$\int_{0}^{1} (a x^{2} + b) d x$
82507	Evaluate the Limit	limit as x approaches infinity of 10-2/(x^2)	$lim_{x \to \infty} 10 - \frac{2}{x^{2}}$
82508	Find the Derivative - d/da	a=1/2bh	$a = \frac{1}{2} b h$
82509	Evaluate the Integral	integral of x^2(2x+5)^2 with respect to x	$\int x^{2} {(2 x + 5)}^{2} d x$
82510	Find the Domain and Range	g(x)=3,x<=2; x/2+3,x>2	$g (x) = {\begin{cases} 3, x \leq 2 \\ \frac{x}{2} + 3, x > 2 \end{cases}$
82511	Evaluate the Limit	limit as x approaches 1 of ((-6x+1)/8)^3	$lim_{x \to 1} {(\frac{- 6 x + 1}{8})}^{3}$
82512	Evaluate the Limit	limit as x approaches negative infinity of (7x^3-4x+2x^6)/(5x^3-3x^2)	$lim_{x \to - \infty} \frac{7 x^{3} - 4 x + 2 x^{6}}{5 x^{3} - 3 x^{2}}$
82513	Find the Derivative - d/dx	y = cube root of x(2x-x^2)	$y = \sqrt[3]{x} (2 x - x^{2})$
82514	Find the Antiderivative	f(x)=3/( cube root of x+3)	$f (x) = \frac{3}{\sqrt[3]{x + 3}}$
82515	Find the Maximum/Minimum Value	h(x)=x^4-3x^2+x	$h (x) = x^{4} - 3 x^{2} + x$
82516	Find the Antiderivative	2/( square root of x+3)-sin(2x)^2	$\frac{2}{\sqrt{x + 3}} - \sin^{2} (2 x)$
82517	Find the Maximum/Minimum Value	f(x)=-x^5+4x^3-2x+2	$f (x) = - x^{5} + 4 x^{3} - 2 x + 2$
82518	Find the Derivative - d/dx	4 natural log of -2-x	$4 \ln (- 2 - x)$
82519	Find Where Increasing/Decreasing	f(x)=-1/3x^6	$f (x) = - \frac{1}{3} x^{6}$
82520	Find the Antiderivative	e^(-3x)-4x+50	$e^{- 3 x} - 4 x + 50$
82521	Find dy/dx	-xy=4+5y	$- x y = 4 + 5 y$
82522	Find the Antiderivative	2/(5-2x)+2/x+3/(x^2)	$\frac{2}{5 - 2 x} + \frac{2}{x} + \frac{3}{x^{2}}$
82523	Find the Derivative - d/dx	y^(xy)	$y^{x y}$
82524	Find the Inflection Points	e^(-x)+2xe^(-x)+x^2e^(-x)	$e^{- x} + 2 x e^{- x} + x^{2} e^{- x}$
82525	Evaluate the Integral	integral of x(3x+2)(x-3) with respect to x	$\int x (3 x + 2) (x - 3) d x$
82526	Find dy/dx	-1-x^3+xy+3y=0	$- 1 - x^{3} + x y + 3 y = 0$
82527	Find the Derivative - d/dx	y=cos(4x+5)	$y = \cos (4 x + 5)$
82528	Integrate Using u-Substitution	integral of (x^2-1)/( square root of 2x-1) with respect to x	$\int \frac{x^{2} - 1}{\sqrt{2 x - 1}} d x$
82529	Find the Antiderivative	(x-1)/x	$\frac{x - 1}{x}$
82530	Evaluate the Integral	integral of 5(3-cos(x)^2)^-6sin(2x) with respect to x	$\int 5 {(3 - \cos^{2} (x))}^{- 6} \sin (2 x) d x$
82531	Evaluate the Limit	limit as x approaches 1 of (-e^x)/(x+4x^2)	$lim_{x \to 1} \frac{- e^{x}}{x + 4 x^{2}}$
82532	Find dy/dx	xy-x^3=2y^3	$x y - x^{3} = 2 y^{3}$
82533	Find the Derivative - d/dx	302.2((103^x)/(100^x))	$302.2 (\frac{103^{x}}{100^{x}})$
82534	Find the Second Derivative	sin(x)-cos(x)	$\sin (x) - \cos (x)$
82535	Evaluate the Integral	integral from (2 square root of 3)/3 to 2 of 12/(x square root of 9x^2-9) with respect to x	$\int_{\frac{2 \sqrt{3}}{3}}^{2} \frac{12}{x \sqrt{9 x^{2} - 9}} d x$
82536	Evaluate the Integral	integral from -1/2 to 0 of 14/( square root of 25-25x^2) with respect to x	$\int_{- \frac{1}{2}}^{0} \frac{14}{\sqrt{25 - 25 x^{2}}} d x$
82537	Find the Second Derivative	y=1/2x^2-x^4+x-1/4x^5	$y = \frac{1}{2} x^{2} - x^{4} + x - \frac{1}{4} x^{5}$
82538	Evaluate the Integral	integral of (2x^4+x+3x^2) with respect to x	$\int (2 x^{4} + x + 3 x^{2}) d x$
82539	Find the Integral	-1/2e^(-2x)	$- \frac{1}{2} e^{- 2 x}$
82540	Find the Derivative - d/dh	S=( square root of hw)/60	$S = \frac{\sqrt{h w}}{60}$
82541	Evaluate the Integral	integral from 0 to 1 of (6x+2)/((x+1)(2x+1)) with respect to x	$\int_{0}^{1} \frac{6 x + 2}{(x + 1) (2 x + 1)} d x$
82542	Evaluate the Integral	pi integral from 0 to 1 of (9-6x+x^2) with respect to x	$π \int_{0}^{1} (9 - 6 x + x^{2}) d x$
82543	Find the Derivative - d/dx	( natural log of square root of x)/x	$\frac{\ln (\sqrt{x})}{x}$
82544	Evaluate the Integral	integral of ( cube root of natural log of x)/x with respect to x	$\int \frac{\sqrt[3]{\ln (x)}}{x} d x$
82545	Find the Derivative - d/dx	y=e^(-x)cosh(x)	$y = e^{- x} \cosh (x)$
82546	Evaluate Using L'Hospital's Rule	limit as x approaches 4 of (x-4)/( square root of x-2)	$lim_{x \to 4} \frac{x - 4}{\sqrt{x} - 2}$
82547	Evaluate Using L'Hospital's Rule	limit as x approaches 1 of (3cos(2x-2)-3x^2)/(3 natural log of 3-2x)	$lim_{x \to 1} \frac{3 \cos (2 x - 2) - 3 x^{2}}{3 \ln (3 - 2 x)}$
82548	Find the Antiderivative	1+tan(x/2)^2	$1 + \tan^{2} (\frac{x}{2})$
82549	Find the Maximum/Minimum Value	f(x)=-1/2x^4+2x^3+40x^2-13	$f (x) = - \frac{1}{2} x^{4} + 2 x^{3} + 40 x^{2} - 13$
82550	Find dy/dx	-y^2-y=2x^3	$- y^{2} - y = 2 x^{3}$
82551	Find the Inflection Points	-1/6x^6-x^5-5/3x^4	$- \frac{1}{6} x^{6} - x^{5} - \frac{5}{3} x^{4}$
82552	Find the Derivative - d/dx	(1-x^2)^(-1/2)	${(1 - x^{2})}^{- \frac{1}{2}}$
82553	Evaluate the Integral	integral of (e^(2/x))/(3x^2) with respect to x	$\int \frac{e^{\frac{2}{x}}}{3 x^{2}} d x$
82554	Find dy/dx	-3y+xy=x^3	$- 3 y + x y = x^{3}$
82555	Find the Derivative - d/dx	2x+cos(x)	$2 x + \cos (x)$
82556	Find dy/dx	-4x^3-y^3=4y^2	$- 4 x^{3} - y^{3} = 4 y^{2}$
82557	Evaluate the Integral	integral from 5 to infinity of 1/(t^2-4t) with respect to t	$\int_{5}^{\infty} \frac{1}{t^{2} - 4 t} d t$
82558	Integrate Using u-Substitution	integral of xcos(x^2) with respect to x	$\int x \cos (x^{2}) d x$
82559	Find Where Increasing/Decreasing	f'(x)=((x-2)^3)/x	$f' (x) = \frac{{(x - 2)}^{3}}{x}$
82560	Evaluate the Integral	integral from 0 to a of 8x square root of a^2-x^2 with respect to x	$\int_{0}^{a} 8 x \sqrt{a^{2} - x^{2}} d x$
82561	Find the Derivative - d/dx	sec( square root of x)^2	$\sec^{2} (\sqrt{x})$
82562	Find Where Increasing/Decreasing	f(x)=- cube root of 2x^5	$f (x) = - \sqrt[3]{2 x^{5}}$
82563	Find the Antiderivative	f(x)=5-3(1+x^2)^-1	$f (x) = 5 - 3 {(1 + x^{2})}^{- 1}$
82564	Find the Derivative - d/dh	limit as h approaches 0 of ((h-3)^2-9)/h	$lim_{h \to 0} \frac{{(h - 3)}^{2} - 9}{h}$
82565	Evaluate the Summation	sum from r=0 to 7 of r^2(-x)^r	$\sum_{r = 0}^{7} r^{2} {(- x)}^{r}$
82566	Evaluate the Integral	integral from 1 to 8 of ( cube root of x-1/x) with respect to x	$\int_{1}^{8} (\sqrt[3]{x} - \frac{1}{x}) d x$
82567	Find the Antiderivative	f(x)=2e^(4x-6)-2x^3	$f (x) = 2 e^{4 x - 6} - 2 x^{3}$
82568	Find the Derivative - d/dx	y=x^3*cos(x^3)	$y = x^{3} \cdot \cos (x^{3})$
82569	Find the Antiderivative	f(x)=2/( square root of x-2)	$f (x) = \frac{2}{\sqrt{x - 2}}$
82570	Find the Integral	e^(x+y)	$e^{x + y}$
82571	Evaluate the Integral	integral of (x^-2-6+x^5) with respect to x	$\int (x^{- 2} - 6 + x^{5}) d x$
82572	Find the Derivative - d/dy	1-xe^y	$1 - x e^{y}$
82573	Evaluate the Limit	limit as x approaches infinity of ((x-1)(3x+1)^3)/((x-2)^4)	$lim_{x \to \infty} \frac{(x - 1) {(3 x + 1)}^{3}}{{(x - 2)}^{4}}$
82574	Find the Integral	xsin(2x)	$x \sin (2 x)$
82575	Find dy/dx	y=sin(6x)cos(x)^2	$y = \sin (6 x) \cos^{2} (x)$
82576	Find the Derivative - d/dx	2e^(1-6)cos(e^(1-6))sin(e^(1-6))+sec(sin(6))^2cos(6)	$2 e^{1 - 6} \cos (e^{1 - 6}) \sin (e^{1 - 6}) + \sec^{2} (\sin (6)) \cos (6)$
82577	Integrate Using u-Substitution	integral of x^2sin(x^3) with respect to x	$\int x^{2} \sin (x^{3}) d x$
82578	Evaluate the Integral	integral from 2 to x of (3t^2-1) with respect to t	$\int_{2}^{x} (3 t^{2} - 1) d t$
82579	Evaluate the Integral	integral of natural log of 1+x^2 with respect to x	$\int \ln (1 + x^{2}) d x$
82580	Find the Derivative - d/dx	(cos(-10x))	$(\cos (- 10 x))$
82581	Find dy/dx	-4y-1-y^3=-3x^2-y^2	$- 4 y - 1 - y^{3} = - 3 x^{2} - y^{2}$
82582	Find dy/dx	2+2x^2+y^2=-5x	$2 + 2 x^{2} + y^{2} = - 5 x$
82583	Find Where Increasing/Decreasing	f(x)=-2(1/2)^x+4	$f (x) = - 2 {(\frac{1}{2})}^{x} + 4$
82584	Find the Maximum/Minimum Value	g(x)=-x^4+3x	$g (x) = - x^{4} + 3 x$
82585	Find the Tangent Line at (1,1)	f(x)=x^3 at (1,1)	$f (x) = x^{3}$ at $(1, 1)$
82586	Find the Derivative - d/dx	(2x+3)^3 square root of 4x^3-1	${(2 x + 3)}^{3} \sqrt{4 x^{3} - 1}$
82587	Evaluate the Limit	limit as x approaches infinity of (1/x)^x	$lim_{x \to \infty} {(\frac{1}{x})}^{x}$
82588	Find the Critical Points	(2x-8)^(2/3)	${(2 x - 8)}^{\frac{2}{3}}$
82589	Evaluate the Integral	integral from 0 to 1 of (1+2x+3x^2) with respect to x	$\int_{0}^{1} (1 + 2 x + 3 x^{2}) d x$
82590	Find the Derivative - d/dx	( cube root of 64x^6)/(x^5)	$\frac{\sqrt[3]{64 x^{6}}}{x^{5}}$
82591	Find the Antiderivative	f'(x)	$f' (x)$
82592	Evaluate the Limit	limit as x approaches 7 of ( fifth root of x+25-2)/(x-7)	$lim_{x \to 7} \frac{\sqrt[5]{x + 25} - 2}{x - 7}$
82593	Evaluate the Limit	limit as x approaches 1 from the left of G(x)	$lim_{x \to 1^{-}} G (x)$
82594	Find the Derivative - d/dw	y=((w^3+4)^5)/8	$y = \frac{{(w^{3} + 4)}^{5}}{8}$
82595	Find the Antiderivative	(x^2-1)^2	${(x^{2} - 1)}^{2}$
82596	Evaluate the Limit	limit as x approaches 1 of (x^3+x^2-2)/(x-1)	$lim_{x \to 1} \frac{x^{3} + x^{2} - 2}{x - 1}$
82597	Evaluate the Integral	integral of sin(x)(4csc(x)-cot(x)) with respect to x	$\int \sin (x) (4 \csc (x) - \cot (x)) d x$
82598	Find the Antiderivative	(4x+11)/(x^2+5x+6)	$\frac{4 x + 11}{x^{2} + 5 x + 6}$
82599	Find the Maximum/Minimum Value	f(x)=4/3x^3+7x^2-8x-42	$f (x) = \frac{4}{3} x^{3} + 7 x^{2} - 8 x - 42$
82600	Find the Derivative - d/dx	(e^x+x)^(1/x)	${(e^{x} + x)}^{\frac{1}{x}}$