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Popular Calculus Problems

derivative of 5sec(x)	derivative\:5\sec(x)
derivative of y=2x^3+3x^2-12x+2	derivative\:y=2x^{3}+3x^{2}-12x+2
integral of xsqrt(x-4)	\int\:x\sqrt{x-4}dx
derivative of f(x)=(sin(t))/t	derivative\:f(x)=\frac{\sin(t)}{t}
(dy)/(dx)=(x-2)(y-2)	\frac{dy}{dx}=(x-2)(y-2)
sum from n=2 to infinity of (-1)^n 1/n	\sum\:_{n=2}^{\infty\:}(-1)^{n}\frac{1}{n}
integral of 1/(5x+x^2)	\int\:\frac{1}{5x+x^{2}}dx
limit as x approaches+0 of xln(x)	\lim\:_{x\to\:+0}(x\ln(x))
tangent of f(x)=sqrt(x+5),(4,3)	tangent\:f(x)=\sqrt{x+5},(4,3)
derivative of sqrt(25-x^2-y^2)	\frac{d}{dx}(\sqrt{25-x^{2}-y^{2}})
tangent of f(x)=(x^2)/(x+8),(1, 1/9)	tangent\:f(x)=\frac{x^{2}}{x+8},(1,\frac{1}{9})
y^'=y^2+1	y^{\prime\:}=y^{2}+1
derivative of f(x)=xsqrt(4-x)	derivative\:f(x)=x\sqrt{4-x}
derivative of sqrt(2x+3y)	\frac{d}{dx}(\sqrt{2x+3y})
limit as x approaches 2pi of (sin(x))/x	\lim\:_{x\to\:2π}(\frac{\sin(x)}{x})
(\partial)/(\partial y)(xln(xy))	\frac{\partial\:}{\partial\:y}(x\ln(xy))
sum from n=1 to infinity of (cos(npi))/n	\sum\:_{n=1}^{\infty\:}\frac{\cos(nπ)}{n}
limit as t approaches 0 of (e^{-1t}-1)/t	\lim\:_{t\to\:0}(\frac{e^{-1t}-1}{t})
implicit (dy)/(dx),-x/y =0	implicit\:\frac{dy}{dx},-\frac{x}{y}=0
derivative of (1-2x^{-1})	\frac{d}{dx}((1-2x)^{-1})
integral of (sec(3x)+csc(3x))^2	\int\:(\sec(3x)+\csc(3x))^{2}dx
integral of (x^2-4)/(x^3-3x^2-x+3)	\int\:\frac{x^{2}-4}{x^{3}-3x^{2}-x+3}dx
integral of x/(\sqrt[3]{x^2+9)}	\int\:\frac{x}{\sqrt[3]{x^{2}+9}}dx
derivative of (4-t)(4+t^3)^{-1}	derivative\:(4-t)(4+t^{3})^{-1}
(\partial)/(\partial y)(4/3 pi(x^3-y^3))	\frac{\partial\:}{\partial\:y}(\frac{4}{3}π(x^{3}-y^{3}))
limit as x approaches infinity of 3/(5x)	\lim\:_{x\to\:\infty\:}(\frac{3}{5x})
integral of 9e^{3x}	\int\:9e^{3x}dx
integral of xe^{3x}+e^x	\int\:xe^{3x}+e^{x}dx
derivative of f(x)=e^{2x}(x^3+1)	derivative\:f(x)=e^{2x}(x^{3}+1)
(d^2)/(dx^2)((4x^2+9x)cos(x))	\frac{d^{2}}{dx^{2}}((4x^{2}+9x)\cos(x))
e^xy*(dy)/(dx)=e^{-y}+e^{-2x-y}	e^{x}y\cdot\:\frac{dy}{dx}=e^{-y}+e^{-2x-y}
integral of 1/((1+sqrt(x))^{3/2)}	\int\:\frac{1}{(1+\sqrt{x})^{\frac{3}{2}}}dx
(d^3y)/(dx^3)=4x^3+x	\frac{d^{3}y}{dx^{3}}=4x^{3}+x
(d^2)/(dx^2)(6/(7x^4))	\frac{d^{2}}{dx^{2}}(\frac{6}{7x^{4}})
integral of 2pix^3sqrt(1+9x^4)	\int\:2πx^{3}\sqrt{1+9x^{4}}dx
(\partial)/(\partial l)(9l^{2/3}k^{1/3})	\frac{\partial\:}{\partial\:l}(9l^{\frac{2}{3}}k^{\frac{1}{3}})
y^{''}+9y=24sin(3t)	y^{\prime\:\prime\:}+9y=24\sin(3t)
integral of (2^{x+1})/(10^x)	\int\:\frac{2^{x+1}}{10^{x}}dx
integral of (1+sin(x))/(cos^2(x))	\int\:\frac{1+\sin(x)}{\cos^{2}(x)}dx
derivative of \sqrt[3]{ln(4-x^2)}	derivative\:\sqrt[3]{\ln(4-x^{2})}
y^'=(ln(2))/7 y-20,y(0)=200	y^{\prime\:}=\frac{\ln(2)}{7}y-20,y(0)=200
derivative of w/(w+d/w)	derivative\:\frac{w}{w+\frac{d}{w}}
derivative of \sqrt[4]{y-2x}	\frac{d}{dx}(\sqrt[4]{y-2x})
derivative of f(x)=\sqrt[3]{36x^2+10}	derivative\:f(x)=\sqrt[3]{36x^{2}+10}
(\partial)/(\partial x)(-2x-8y+18)	\frac{\partial\:}{\partial\:x}(-2x-8y+18)
derivative of cos(arccos(x))	\frac{d}{dx}(\cos(\arccos(x)))
derivative of 1/2 (x-1/2 sin(2x))	\frac{d}{dx}(\frac{1}{2}(x-\frac{1}{2}\sin(2x)))
derivative of ((x+3)/(x-2))^3	derivative\:(\frac{x+3}{x-2})^{3}
(\partial)/(\partial y)(3x^2y-y^3)	\frac{\partial\:}{\partial\:y}(3x^{2}y-y^{3})
derivative of x^2arctan(ln(x))	\frac{d}{dx}(x^{2}\arctan(\ln(x)))
derivative of e^{x^2-9}	derivative\:e^{x^{2}-9}
derivative of 2x^4-x^3+6x^2	derivative\:2x^{4}-x^{3}+6x^{2}
derivative of a(t)=t^3-12t	derivative\:a(t)=t^{3}-12t
integral of+x^2sqrt(a^2-x^2)	\int\:+x^{2}\sqrt{a^{2}-x^{2}}dx
integral of (e^{9sqrt(t)})/(sqrt(t))	\int\:\frac{e^{9\sqrt{t}}}{\sqrt{t}}dt
derivative of arcsin(x)+sqrt(1+x^2)	derivative\:\arcsin(x)+\sqrt{1+x^{2}}
integral from 0 to 5 of (25-x^2)	\int\:_{0}^{5}(25-x^{2})dx
limit as x approaches 0 of 1/x-csc(x)	\lim\:_{x\to\:0}(\frac{1}{x}-\csc(x))
integral from 0 to pi of 9x^2sin(1/2 x)	\int\:_{0}^{π}9x^{2}\sin(\frac{1}{2}x)dx
(\partial)/(\partial x)(-1/(x^2)+e^{-y})	\frac{\partial\:}{\partial\:x}(-\frac{1}{x^{2}}+e^{-y})
(dy)/(dx)=y(1+x)^{-1}	\frac{dy}{dx}=y(1+x)^{-1}
integral of 1/((x+3)(x+5))	\int\:\frac{1}{(x+3)(x+5)}dx
(\partial)/(\partial x)((5x-x^2)cos(t))	\frac{\partial\:}{\partial\:x}((5x-x^{2})\cos(t))
inverse oflaplace Y(s)=(s-2)/(s^2-2s-3)	inverselaplace\:Y(s)=\frac{s-2}{s^{2}-2s-3}
tangent of f(x)=-3x^2+x+2,\at x=1	tangent\:f(x)=-3x^{2}+x+2,\at\:x=1
(\partial)/(\partial x)(p/(1+e^{cos(x))})	\frac{\partial\:}{\partial\:x}(\frac{p}{1+e^{\cos(x)}})
integral of (3x+4)/(sqrt(2x+x^2))	\int\:\frac{3x+4}{\sqrt{2x+x^{2}}}dx
integral of \sqrt[3]{x-1}	\int\:\sqrt[3]{x-1}dx
derivative of (y^3)/3+1/(4y)	derivative\:\frac{y^{3}}{3}+\frac{1}{4y}
integral from 4 to 5 of (sqrt(x-4))/x	\int\:_{4}^{5}\frac{\sqrt{x-4}}{x}dx
(\partial)/(\partial x)(x^2+3xy+y^2+1)	\frac{\partial\:}{\partial\:x}(x^{2}+3xy+y^{2}+1)
integral of 1/(3-2y)	\int\:\frac{1}{3-2y}dy
(\partial)/(\partial x)((sqrt(x))^x)	\frac{\partial\:}{\partial\:x}((\sqrt{x})^{x})
derivative of 3e^{-x}	derivative\:3e^{-x}
(\partial)/(\partial y)(sin(x/(1+y)))	\frac{\partial\:}{\partial\:y}(\sin(\frac{x}{1+y}))
sum from n=0 to infinity of 1/(n^6)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{6}}
integral of x/((1-x))	\int\:\frac{x}{(1-x)}dx
integral of-4x^2	\int\:-4x^{2}dx
derivative of log_{10}(sqrt(x))	\frac{d}{dx}(\log_{10}(\sqrt{x}))
f(x)=4e^xcos(x)	f(x)=4e^{x}\cos(x)
integral of 1/((ax+b))	\int\:\frac{1}{(ax+b)}dx
derivative of e^{x^2}+5x^2	derivative\:e^{x^{2}}+5x^{2}
integral of (-x^2+x)/(x^4)	\int\:\frac{-x^{2}+x}{x^{4}}dx
integral of 1/(5+3cos(x))	\int\:\frac{1}{5+3\cos(x)}dx
derivative of ln\|cos(pi/x \|)	\frac{d}{dx}(\ln\left\|\cos(\frac{π}{x})\right\|)
integral from 0 to 4 of sqrt(5)	\int\:_{0}^{4}\sqrt{5}dx
integral of (x^3)/(sqrt(x^2-1))	\int\:\frac{x^{3}}{\sqrt{x^{2}-1}}dx
parity sqrt(25-x^2)dx	parity\:\sqrt{25-x^{2}}dx
(\partial)/(\partial y)(xe^{2yz})	\frac{\partial\:}{\partial\:y}(xe^{2yz})
(\partial)/(\partial s)(s/(sqrt(s^2+t^2)))	\frac{\partial\:}{\partial\:s}(\frac{s}{\sqrt{s^{2}+t^{2}}})
(dy)/(dx)=((x^2))/(y^2)	\frac{dy}{dx}=\frac{(x^{2})}{y^{2}}
(\partial)/(\partial z)(z^2)	\frac{\partial\:}{\partial\:z}(z^{2})
y^'+(1/t)y=3cos(2t)	y^{\prime\:}+(\frac{1}{t})y=3\cos(2t)
derivative of log_{5}(3x^2-7x)	\frac{d}{dx}(\log_{5}(3x^{2}-7x))
integral of (7x+29)/(x^2+8x+15)	\int\:\frac{7x+29}{x^{2}+8x+15}dx
taylor f(x)=x^2-2x+4	taylor\:f(x)=x^{2}-2x+4
(\partial)/(\partial x)(xln(z^7+x^7))	\frac{\partial\:}{\partial\:x}(x\ln(z^{7}+x^{7}))
derivative of x(x^4+2)^3	derivative\:x(x^{4}+2)^{3}
derivative of sec(θ)tan(θ)	derivative\:\sec(θ)\tan(θ)
derivative of log_{1}(x)	\frac{d}{dx}(\log_{1}(x))

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