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Popular Calculus Problems

tangent of f(x)=-2xcos(x),(pi,2pi)	tangent\:f(x)=-2x\cos(x),(π,2π)
sum from n=0 to infinity of n!2^n	\sum\:_{n=0}^{\infty\:}n!2^{n}
5sqrt(xy)((dy)/(dx))=4	5\sqrt{xy}(\frac{dy}{dx})=4
derivative of 5e^{-0.5x}+100	\frac{d}{dx}(5e^{-0.5x}+100)
integral of (2^{18x})/4	\int\:\frac{2^{18x}}{4}dx
area y=4-x^2,y=16-7x	area\:y=4-x^{2},y=16-7x
(x^2+4)(dy)/(dx)=2x-8xy	(x^{2}+4)\frac{dy}{dx}=2x-8xy
(e^{x+y}+ye^y)dx+(xe^y-1)dy=0	(e^{x+y}+ye^{y})dx+(xe^{y}-1)dy=0
inverse oflaplace (s+1)/(s^2+2s+5)	inverselaplace\:\frac{s+1}{s^{2}+2s+5}
derivative of (x^2/(9-x^2))	\frac{d}{dx}(\frac{x^{2}}{9-x^{2}})
(\partial)/(\partial x)(2yx)	\frac{\partial\:}{\partial\:x}(2yx)
integral of (x^2)/(sqrt(x^2-x+1))	\int\:\frac{x^{2}}{\sqrt{x^{2}-x+1}}dx
integral of x^4sqrt(9+x^5)	\int\:x^{4}\sqrt{9+x^{5}}dx
integral of 11x^{4/7}+4x^{-6/7}	\int\:11x^{\frac{4}{7}}+4x^{-\frac{6}{7}}dx
derivative of (x^2/7)	\frac{d}{dx}(\frac{x^{2}}{7})
tangent of f(x)=2x^3-4x^2,\at x=1	tangent\:f(x)=2x^{3}-4x^{2},\at\:x=1
integral from 1 to 5 of 5/(x^2+4x+4)	\int\:_{1}^{5}\frac{5}{x^{2}+4x+4}dx
(\partial)/(\partial y)((x^2)/(1+y^3))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}}{1+y^{3}})
derivative of axe^{bx^2}	\frac{d}{dx}(axe^{bx^{2}})
(\partial)/(\partial x)(3x^2+6xy)	\frac{\partial\:}{\partial\:x}(3x^{2}+6xy)
derivative of (12(3x^3-16)/(4x-x^4))	\frac{d}{dx}(\frac{12(3x^{3}-16)}{4x-x^{4}})
integral of p(p+7)^8	\int\:p(p+7)^{8}dp
y^{''}+2y^'+y=4e^{-1}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=4e^{-1}
d/(dt)(tan(t+pi/4))	\frac{d}{dt}(\tan(t+\frac{π}{4}))
(dy)/(dx)=y-y^5	\frac{dy}{dx}=y-y^{5}
(d^2y)/(dx^2)-2*(dy)/(dx)+ay=0,a>1	\frac{d^{2}y}{dx^{2}}-2\cdot\:\frac{dy}{dx}+ay=0,a>1
derivative of (x^5+1)/x	derivative\:\frac{x^{5}+1}{x}
integral from 0 to 1 of (8y)/(e^{2y)}	\int\:_{0}^{1}\frac{8y}{e^{2y}}dy
integral from 0 to 1 of 2pix(x^3-x^4)	\int\:_{0}^{1}2πx(x^{3}-x^{4})dx
integral of x/((x-3)^2)	\int\:\frac{x}{(x-3)^{2}}dx
(\partial)/(\partial x)((y^2)/(4-x^2))	\frac{\partial\:}{\partial\:x}(\frac{y^{2}}{4-x^{2}})
derivative of (sinh(x)^{2x^2+2x})	\frac{d}{dx}((\sinh(x))^{2x^{2}+2x})
integral of ((ln(x))^2)/2	\int\:\frac{(\ln(x))^{2}}{2}dx
y^'=6y^2+xy^2,y(0)=1	y^{\prime\:}=6y^{2}+xy^{2},y(0)=1
(d^2)/(dx^2)((2000t)/(4t+75))	\frac{d^{2}}{dx^{2}}(\frac{2000t}{4t+75})
implicit xy=2	implicit\:xy=2
derivative of (5sqrt(x)^{ln(x)})	\frac{d}{dx}((5\sqrt{x})^{\ln(x)})
integral of sqrt(sin(2x))cos(2x)	\int\:\sqrt{\sin(2x)}\cos(2x)dx
derivative of f(x)= 1/5 x-1/2	derivative\:f(x)=\frac{1}{5}x-\frac{1}{2}
integral of 8x^7	\int\:8x^{7}dx
(x^{3/2})/3	\frac{x^{\frac{3}{2}}}{3}
inverse oflaplace (e^{-2s})/(s(3s+2))	inverselaplace\:\frac{e^{-2s}}{s(3s+2)}
(\partial)/(\partial y)(sqrt(y-x))	\frac{\partial\:}{\partial\:y}(\sqrt{y-x})
derivative of (x^2)/9	derivative\:\frac{x^{2}}{9}
integral from 0 to 1 of x/(sqrt(x^2+1))	\int\:_{0}^{1}\frac{x}{\sqrt{x^{2}+1}}dx
derivative of 1+2sin((x^2/2))	\frac{d}{dx}(1+2\sin(\frac{x^{2}}{2}))
integral of 4/(x^2+16)	\int\:\frac{4}{x^{2}+16}dx
integral of (2(x+2))/5	\int\:\frac{2(x+2)}{5}dx
tangent of f(x)=(x^3+2)/3 ,\at x=-3	tangent\:f(x)=\frac{x^{3}+2}{3},\at\:x=-3
derivative of x^4+y^4	\frac{d}{dx}(x^{4}+y^{4})
derivative of x/(x^3+1)	\frac{d}{dx}(\frac{x}{x^{3}+1})
derivative of f(x)=cos^2(2x)	derivative\:f(x)=\cos^{2}(2x)
derivative of sqrt((1-2x)/(1+2x))	derivative\:\sqrt{\frac{1-2x}{1+2x}}
derivative of 3^x-2	\frac{d}{dx}(3^{x}-2)
derivative of e^{x^2}y	\frac{d}{dx}(e^{x^{2}}y)
integral of 1/3 x^2	\int\:\frac{1}{3}x^{2}dx
limit as x approaches 0 of x^3+x	\lim\:_{x\to\:0}(x^{3}+x)
integral of 2/((x^2+1)^{3/2)}	\int\:\frac{2}{(x^{2}+1)^{\frac{3}{2}}}dx
derivative of sqrt((1-3x/(2x+1)))	\frac{d}{dx}(\sqrt{\frac{1-3x}{2x+1}})
limit as x approaches pi/6 of sin(x)	\lim\:_{x\to\:\frac{π}{6}}(\sin(x))
(\partial)/(\partial y)(1/(e^{x^2+y^2)})	\frac{\partial\:}{\partial\:y}(\frac{1}{e^{x^{2}+y^{2}}})
integral of (x^3)/((2+3x^4)^3)	\int\:\frac{x^{3}}{(2+3x^{4})^{3}}dx
sum from n=1 to infinity of 7/n	\sum\:_{n=1}^{\infty\:}\frac{7}{n}
(\partial)/(\partial x)(sqrt(3-3x^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{3-3x^{2}+y^{2}})
(8+x)y^'=5y	(8+x)y^{\prime\:}=5y
inverse oflaplace (10)/((s(s^2+2s+20)))	inverselaplace\:\frac{10}{(s(s^{2}+2s+20))}
derivative of x^2+2^x	\frac{d}{dx}(x^{2}+2^{x})
integral of (1+tan(x))^5sec^2(x)	\int\:(1+\tan(x))^{5}\sec^{2}(x)dx
derivative of y=3cos(2x)	derivative\:y=3\cos(2x)
integral from 1 to 4 of (x-3)^2	\int\:_{1}^{4}(x-3)^{2}dx
xy^'+y=8xy^2,y(1)=3	xy^{\prime\:}+y=8xy^{2},y(1)=3
derivative of cos(2*x)	\frac{d}{dx}(\cos(2\cdot\:x))
tangent of y=8sqrt(x),(4,16)	tangent\:y=8\sqrt{x},(4,16)
(\partial)/(\partial x)((75-x) 1/3 pix^2)	\frac{\partial\:}{\partial\:x}((75-x)\frac{1}{3}πx^{2})
(\partial)/(\partial x)(xln(y)+1/9 x^3)	\frac{\partial\:}{\partial\:x}(x\ln(y)+\frac{1}{9}x^{3})
derivative of sqrt(x)-3	derivative\:\sqrt{x}-3
limit as x approaches 9-of 7/(x-9)	\lim\:_{x\to\:9-}(\frac{7}{x-9})
integral from 0 to pi of 7cos^6(x)	\int\:_{0}^{π}7\cos^{6}(x)dx
derivative of y=xsin(4/x)	derivative\:y=x\sin(\frac{4}{x})
integral from 1 to 3 of (1+2x-4x^3)	\int\:_{1}^{3}(1+2x-4x^{3})dx
inverse oflaplace 1/((s^2+3s+2)(s+1))	inverselaplace\:\frac{1}{(s^{2}+3s+2)(s+1)}
derivative of y=(x^3)/3-x^2-3x	derivative\:y=\frac{x^{3}}{3}-x^{2}-3x
integral of (x^2+4x-7)/(x-1)	\int\:\frac{x^{2}+4x-7}{x-1}dx
derivative of (8x-1/(6x+7))	\frac{d}{dx}(\frac{8x-1}{6x+7})
integral of-ln(x)-(ln(x))/4	\int\:-\ln(x)-\frac{\ln(x)}{4}dx
integral from-2 to 4 of \|t^2-2t-3\|	\int\:_{-2}^{4}\left\|t^{2}-2t-3\right\|dt
f^'(x)=2x^2+3x-2	f^{\prime\:}(x)=2x^{2}+3x-2
(\partial)/(\partial x)(x^4y-x^2y^3)	\frac{\partial\:}{\partial\:x}(x^{4}y-x^{2}y^{3})
derivative of y=3x^2+(4x)/3-2	derivative\:y=3x^{2}+\frac{4x}{3}-2
derivative of 3/(r^3)	derivative\:\frac{3}{r^{3}}
(dy}{dx}=\frac{1-y^2)/x	\frac{dy}{dx}=\frac{1-y^{2}}{x}
integral of (tan^3(2/z))/(z^2)	\int\:\frac{\tan^{3}(\frac{2}{z})}{z^{2}}
(dy)/(dx)+xy=y^4	\frac{dy}{dx}+xy=y^{4}
integral of (x+9)/(x^2+9)	\int\:\frac{x+9}{x^{2}+9}dx
(\partial)/(\partial x)((x^2-3y)(x-2))	\frac{\partial\:}{\partial\:x}((x^{2}-3y)(x-2))
(\partial)/(\partial y)((e^x)/(e^x+e^y))	\frac{\partial\:}{\partial\:y}(\frac{e^{x}}{e^{x}+e^{y}})
(\partial)/(\partial x)(5x^3y+3sin(xy))	\frac{\partial\:}{\partial\:x}(5x^{3}y+3\sin(xy))
integral of (2^x-2)^2	\int\:(2^{x}-2)^{2}dx
integral of x*cos(x^2+1)	\int\:x\cdot\:\cos(x^{2}+1)dx
integral of (3x-1)/(4x^2-4x+17)	\int\:\frac{3x-1}{4x^{2}-4x+17}dx

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