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Popular Calculus Problems

derivative of y=4x^3-20x+25	derivative\:y=4x^{3}-20x+25
derivative of 15x^2-15x^4	\frac{d}{dx}(15x^{2}-15x^{4})
integral of 1/((x-6)^2)	\int\:\frac{1}{(x-6)^{2}}dx
(\partial)/(\partial x)(sin(x^2)+xy^3)	\frac{\partial\:}{\partial\:x}(\sin(x^{2})+xy^{3})
derivative of f(x)=(1+csc(x^3))/(1-cot(x^3))	derivative\:f(x)=\frac{1+\csc(x^{3})}{1-\cot(x^{3})}
integral of (4-x)^3	\int\:(4-x)^{3}dx
sum from n=1 to infinity of (n^2)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{n^{2}}{n+1}
derivative of y=-x/(9y)	derivative\:y=-\frac{x}{9y}
d/(dt)(-4t^2+176t+100)	\frac{d}{dt}(-4t^{2}+176t+100)
derivative of sec(x^2+2)	\frac{d}{dx}(\sec(x^{2}+2))
integral from pi/9 to infinity of 2/x	\int\:_{\frac{π}{9}}^{\infty\:}\frac{2}{x}dx
sum from n=2 to infinity of 5/(7^n)	\sum\:_{n=2}^{\infty\:}\frac{5}{7^{n}}
(\partial)/(\partial y)(4x^2y^3)	\frac{\partial\:}{\partial\:y}(4x^{2}y^{3})
(\partial)/(\partial x)(ln(sqrt(x)))	\frac{\partial\:}{\partial\:x}(\ln(\sqrt{x}))
(d^2)/(dx^2)((x^2)/(e^x))	\frac{d^{2}}{dx^{2}}(\frac{x^{2}}{e^{x}})
(dy)/(dx)=x^4y^{-5}	\frac{dy}{dx}=x^{4}y^{-5}
derivative of y=3xe^{-kx}	derivative\:y=3xe^{-kx}
derivative of 4/(cos(x))	\frac{d}{dx}(\frac{4}{\cos(x)})
integral of-3/25 x+49	\int\:-\frac{3}{25}x+49dx
(\partial)/(\partial z)(2y)	\frac{\partial\:}{\partial\:z}(2y)
laplacetransform e(t)	laplacetransform\:e(t)
limit as x approaches 1 of (x-2)/(\|x-1\|)	\lim\:_{x\to\:1}(\frac{x-2}{\left\|x-1\right\|})
tangent of y=x^4+3x^2-x,(1,3)	tangent\:y=x^{4}+3x^{2}-x,(1,3)
(\partial)/(\partial x)(2y-2yx)	\frac{\partial\:}{\partial\:x}(2y-2yx)
derivative of 3ln(sin(x))	\frac{d}{dx}(3\ln(\sin(x)))
(d^2)/(dt^2)(-9.8t^2+2t+1)	\frac{d^{2}}{dt^{2}}(-9.8t^{2}+2t+1)
y^'=(3x^2+4x-4)/(2y-4),y(1)=3	y^{\prime\:}=\frac{3x^{2}+4x-4}{2y-4},y(1)=3
derivative of (x+8)^2	derivative\:(x+8)^{2}
derivative of 6sin(x+6cos(x))	\frac{d}{dx}(6\sin(x)+6\cos(x))
integral of xln(x)ln(x)	\int\:x\ln(x)\ln(x)dx
derivative of 1/4	derivative\:\frac{1}{4}
integral of log_{3}(x)	\int\:\log_{3}(x)dx
integral of 5arctan(sqrt(x))	\int\:5\arctan(\sqrt{x})dx
(\partial)/(\partial x)(-e^{-2t}sin(x))	\frac{\partial\:}{\partial\:x}(-e^{-2t}\sin(x))
integral of 1/8 e^{-1/8 x}	\int\:\frac{1}{8}e^{-\frac{1}{8}x}dx
limit as x approaches 7 of 2x	\lim\:_{x\to\:7}(2x)
integral of (12.5-0.02x)	\int\:(12.5-0.02x)dx
integral of (cos(5x))^2	\int\:(\cos(5x))^{2}dx
sum from n=1 to infinity of 4/(n^2+3n+2)	\sum\:_{n=1}^{\infty\:}\frac{4}{n^{2}+3n+2}
derivative of 2sqrt(e^{(sin(x)/3)+1})	\frac{d}{dx}(2\sqrt{e^{\frac{\sin(x)}{3}}+1})
taylor sin(pi/2-x)	taylor\:\sin(\frac{π}{2}-x)
limit as x approaches-1-of x^2	\lim\:_{x\to\:-1-}(x^{2})
limit as x approaches 3-of (x^2)/(x-3)	\lim\:_{x\to\:3-}(\frac{x^{2}}{x-3})
integral of 6x^{2/3}	\int\:6x^{\frac{2}{3}}dx
(2x+5)(y^2+4)dx-4y(x^2+5x+6)dy=0	(2x+5)(y^{2}+4)dx-4y(x^{2}+5x+6)dy=0
integral of e^{(a-s)x}	\int\:e^{(a-s)x}dx
integral of tan^3(8x)sec(8x)	\int\:\tan^{3}(8x)\sec(8x)dx
integral of (10)/(x^4)	\int\:\frac{10}{x^{4}}dx
integral of (6x^2+2x-1)/(3x^2)	\int\:\frac{6x^{2}+2x-1}{3x^{2}}dx
derivative of y/(x^2+y^2+1)	\frac{d}{dx}(\frac{y}{x^{2}+y^{2}+1})
f(x)=x^2e^{4x}	f(x)=x^{2}e^{4x}
derivative of ln(xsec(x))	\frac{d}{dx}(\ln(x)\sec(x))
(dy)/(dx)=3x^2-xy	\frac{dy}{dx}=3x^{2}-xy
integral of x^6cos(x)	\int\:x^{6}\cos(x)dx
derivative of ln(cos(5x))	derivative\:\ln(\cos(5x))
y^{''}-5y^'+4y=0,y(0)=-5,y^'(0)=3	y^{\prime\:\prime\:}-5y^{\prime\:}+4y=0,y(0)=-5,y^{\prime\:}(0)=3
limit as x approaches c of 9/8 (7/8)	\lim\:_{x\to\:c}(\frac{9}{8}(\frac{7}{8}))
integral of 1/(xsqrt(289x^2-289))	\int\:\frac{1}{x\sqrt{289x^{2}-289}}dx
(\partial)/(\partial x)(-xy-x^4-y^4)	\frac{\partial\:}{\partial\:x}(-xy-x^{4}-y^{4})
(\partial)/(\partial x)((e^{x^2}+e^{y^2})^2)	\frac{\partial\:}{\partial\:x}((e^{x^{2}}+e^{y^{2}})^{2})
integral from 0 to pi of sin^2(4x)	\int\:_{0}^{π}\sin^{2}(4x)dx
derivative of ky(x)	\frac{d}{dx}(ky(x))
integral from 0 to 1 of 24+976e^{-0.1x}	\int\:_{0}^{1}24+976e^{-0.1x}dx
integral of 1/(sin(x/2))	\int\:\frac{1}{\sin(\frac{x}{2})}dx
limit as x approaches 2 of 2x^2-4	\lim\:_{x\to\:2}(2x^{2}-4)
integral of x^2ln(100)	\int\:x^{2}\ln(100)dx
integral of x\sqrt[3]{x+c}	\int\:x\sqrt[3]{x+c}dx
integral of-10x^4y^5	\int\:-10x^{4}y^{5}dx
derivative of ln(sqrt(4-x^2))	derivative\:\ln(\sqrt{4-x^{2}})
integral of (1-cos^2(x))/(sin(x))	\int\:\frac{1-\cos^{2}(x)}{\sin(x)}dx
y^'=2x+y	y^{\prime\:}=2x+y
(3y^3+2xy^3)+(3xy^2+3y^2)((dy)/(dx))=0	(3y^{3}+2xy^{3})+(3xy^{2}+3y^{2})(\frac{dy}{dx})=0
derivative of (10)/(ln(x))	derivative\:\frac{10}{\ln(x)}
area 16-x^2,x^2-2,-3,3	area\:16-x^{2},x^{2}-2,-3,3
derivative of f(x)=log_{9}(x)	derivative\:f(x)=\log_{9}(x)
derivative of 4/3 x^3-4x^2-60x+10	\frac{d}{dx}(\frac{4}{3}x^{3}-4x^{2}-60x+10)
area x^{1/4},sqrt(2-x),0	area\:x^{\frac{1}{4}},\sqrt{2-x},0
tangent of y=3e^x	tangent\:y=3e^{x}
tangent of f(x)=x^3-3x^2+1,\at x=2	tangent\:f(x)=x^{3}-3x^{2}+1,\at\:x=2
integral of (ln(ln(x)))/x	\int\:\frac{\ln(\ln(x))}{x}dx
integral from 0 to 5pi of x^3sin(x)	\int\:_{0}^{5π}x^{3}\sin(x)dx
roots pir^2h	roots\:πr^{2}h
integral of x^3-4x	\int\:x^{3}-4xdx
integral of sin^9(x)cos^5(x)	\int\:\sin^{9}(x)\cos^{5}(x)dx
derivative of \sqrt[3]{x^2-1}	\frac{d}{dx}(\sqrt[3]{x^{2}-1})
(dy)/(dx)= x/(y^2)	\frac{dy}{dx}=\frac{x}{y^{2}}
y^{''}+4y+24y=0	y^{\prime\:\prime\:}+4y+24y=0
integral of (8x-7)	\int\:(8x-7)dx
integral of y^2e^{xy^2}+4x^3	\int\:y^{2}e^{xy^{2}}+4x^{3}dx
integral of (x^2+3)^2	\int\:(x^{2}+3)^{2}dx
derivative of 6x^{2/3}	derivative\:6x^{\frac{2}{3}}
integral of e^{-5r}	\int\:e^{-5r}dr
derivative of y=e^{2x-x^2}	derivative\:y=e^{2x-x^{2}}
(dy)/(dx)=(8x)/(7y)	\frac{dy}{dx}=\frac{8x}{7y}
limit as x approaches-infinity of 0/x	\lim\:_{x\to\:-\infty\:}(\frac{0}{x})
integral of ln((1+x)/(1-x))	\int\:\ln(\frac{1+x}{1-x})dx
(\partial}{\partial x}(\frac{x+y^2)/z)	\frac{\partial\:}{\partial\:x}(\frac{x+y^{2}}{z})
derivative of sin(x+1)	derivative\:\sin(x+1)
laplacetransform t^2sin(t)*e^{-2t}	laplacetransform\:t^{2}\sin(t)\cdot\:e^{-2t}
derivative of (1+xye^{xy})	\frac{d}{dx}((1+xy)e^{xy})

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