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Popular Calculus Problems

d/(dt)((t^2)/(10))	\frac{d}{dt}(\frac{t^{2}}{10})
tangent of f(x)= 1/(x^3),\at x=5	tangent\:f(x)=\frac{1}{x^{3}},\at\:x=5
integral of (-x+1)/(x^2+4)	\int\:\frac{-x+1}{x^{2}+4}dx
integral from 2 to infinity of e^{-4p}	\int\:_{2}^{\infty\:}e^{-4p}dp
integral of (cos(x))/(7-sin(x))	\int\:\frac{\cos(x)}{7-\sin(x)}dx
(\partial)/(\partial x)(x^6y-3x^3y^2)	\frac{\partial\:}{\partial\:x}(x^{6}y-3x^{3}y^{2})
integral of 1/(sqrt(9x^2+4))	\int\:\frac{1}{\sqrt{9x^{2}+4}}dx
derivative of (x-6)^{8/9}	derivative\:(x-6)^{\frac{8}{9}}
derivative of y=(1-cos(x))/(sin(x))	derivative\:y=\frac{1-\cos(x)}{\sin(x)}
(\partial)/(\partial y)(6xe^{x^2+y^2})	\frac{\partial\:}{\partial\:y}(6xe^{x^{2}+y^{2}})
(\partial)/(\partial y)(x^2e^{x^2y})	\frac{\partial\:}{\partial\:y}(x^{2}e^{x^{2}y})
tangent of ln(x^2-8x+1)(8)	tangent\:\ln(x^{2}-8x+1)(8)
derivative of e^x-2sin(x)	\frac{d}{dx}(e^{x}-2\sin(x))
integral of ((cot^2(x))/(cos^2(x)))	\int\:(\frac{\cot^{2}(x)}{\cos^{2}(x)})dx
inverse oflaplace ((10/6))/(s(s^2+1/2))	inverselaplace\:\frac{(\frac{10}{6})}{s(s^{2}+\frac{1}{2})}
derivative of 5/(6x^5)	derivative\:\frac{5}{6x^{5}}
2x(dy)/(dx)+2y=x^3y^4	2x\frac{dy}{dx}+2y=x^{3}y^{4}
integral of 18y^2	\int\:18y^{2}dy
integral of-4/(x^3)	\int\:-\frac{4}{x^{3}}dx
integral from 2 to 4 of (x+2)/(x^2+3x-4)	\int\:_{2}^{4}\frac{x+2}{x^{2}+3x-4}dx
derivative of-1/(4sqrt(x^3))	\frac{d}{dx}(-\frac{1}{4\sqrt{x^{3}}})
derivative of (x^2/6-x)	\frac{d}{dx}(\frac{x^{2}}{6}-x)
(\partial}{\partial x}(sin(\frac{3x)/y))	\frac{\partial\:}{\partial\:x}(\sin(\frac{3x}{y}))
derivative of e^{(x^2})	\frac{d}{dx}(e^{(x^{2})})
integral of (x+4)/(x^2+8x)	\int\:\frac{x+4}{x^{2}+8x}dx
xy^'+y=2x	xy^{\prime\:}+y=2x
limit as x approaches-infinity of xe^x	\lim\:_{x\to\:-\infty\:}(xe^{x})
limit as x approaches 0 of 3/(1+e^{1/x)}	\lim\:_{x\to\:0}(\frac{3}{1+e^{\frac{1}{x}}})
integral of (x^2)/(9-x^2)	\int\:\frac{x^{2}}{9-x^{2}}dx
y^'+3x^2y=x^2	y^{\prime\:}+3x^{2}y=x^{2}
tangent of f(x)=x^4-13x^2+36,\at x=-1	tangent\:f(x)=x^{4}-13x^{2}+36,\at\:x=-1
derivative of x^{1/2}*(x^2+x-4)	\frac{d}{dx}(x^{\frac{1}{2}}\cdot\:(x^{2}+x-4))
derivative of c^x	\frac{d}{dx}(c^{x})
derivative of \sqrt[4]{2x+16}	\frac{d}{dx}(\sqrt[4]{2x+16})
limit as x approaches infinity of ln(-x)	\lim\:_{x\to\:\infty\:}(\ln(-x))
2^'	2^{\prime\:}
(dy)/(dx)=((e^{x-y}))/((1+e^x))	\frac{dy}{dx}=\frac{(e^{x-y})}{(1+e^{x})}
y^'+a*y-b=0	y^{\prime\:}+a\cdot\:y-b=0
normal of y=9xe^x,(0,0)	normal\:y=9xe^{x},(0,0)
area y= 1/2 x,y= 6/x ,y=2x	area\:y=\frac{1}{2}x,y=\frac{6}{x},y=2x
limit as x approaches 5-of 3/(x-5)	\lim\:_{x\to\:5-}(\frac{3}{x-5})
limit as x approaches 2-of x-1	\lim\:_{x\to\:2-}(x-1)
derivative of-4*sec^2(4x)	derivative\:-4\cdot\:\sec^{2}(4x)
derivative of f(x)=(cos(x))/(1-sin(x))	derivative\:f(x)=\frac{\cos(x)}{1-\sin(x)}
integral of (2x^3+3x^2-4)/(x^2-4x+3)	\int\:\frac{2x^{3}+3x^{2}-4}{x^{2}-4x+3}dx
d/(dz)(sin^2(z))	\frac{d}{dz}(\sin^{2}(z))
inverse oflaplace 2/(s^2+s-2)	inverselaplace\:\frac{2}{s^{2}+s-2}
inverse oflaplace ((s+1))/(s^2+2s+5)	inverselaplace\:\frac{(s+1)}{s^{2}+2s+5}
integral of (6t-15)/(3t^2-2)	\int\:\frac{6t-15}{3t^{2}-2}dt
integral of (60ln(3^{3^{x+1}}))/(3^x-1)	\int\:\frac{60\ln(3^{3^{x+1}})}{3^{x}-1}dx
derivative of \sqrt[x]{2}	\frac{d}{dx}(\sqrt[x]{2})
integral of x-x^4	\int\:x-x^{4}dx
sum from n=0 to infinity of 2^{-2n}	\sum\:_{n=0}^{\infty\:}2^{-2n}
limit as x approaches 0 of 4^2	\lim\:_{x\to\:0}(4^{2})
derivative of (36/x)	\frac{d}{dx}(\frac{36}{x})
inverse oflaplace (3s+4)/(s^2-1)	inverselaplace\:\frac{3s+4}{s^{2}-1}
derivative of 3x^2-6x-9	\frac{d}{dx}(3x^{2}-6x-9)
tangent of y=2sec(x)-4cos(x)	tangent\:y=2\sec(x)-4\cos(x)
limit as t approaches 0 of (e^{4t}-1)/t	\lim\:_{t\to\:0}(\frac{e^{4t}-1}{t})
derivative of 5x^9-2x^6	derivative\:5x^{9}-2x^{6}
inverse oflaplace 6/(s^5)	inverselaplace\:\frac{6}{s^{5}}
(dy)/(dt)-8/t*y=t^5	\frac{dy}{dt}-\frac{8}{t}\cdot\:y=t^{5}
derivative of ((x^2/(x^2+2))^2)	\frac{d}{dx}((\frac{x^{2}}{x^{2}+2})^{2})
(d^2)/(dx^2)(4x-5x^{3/4})	\frac{d^{2}}{dx^{2}}(4x-5x^{\frac{3}{4}})
integral of-4sin(3x)sin(nx)	\int\:-4\sin(3x)\sin(nx)dx
integral of x^{11}cos(x^6)	\int\:x^{11}\cos(x^{6})dx
limit as x approaches 0 of x^4cos(2/x)	\lim\:_{x\to\:0}(x^{4}\cos(\frac{2}{x}))
integral of csc^3(x)	\int\:\csc^{3}(x)dx
integral of (3e^{3x})/(7+e^{3x)}	\int\:\frac{3e^{3x}}{7+e^{3x}}dx
integral of (sqrt(x)+4)/(\sqrt[3]{x)}	\int\:\frac{\sqrt{x}+4}{\sqrt[3]{x}}dx
derivative of x^3-x^2-6x+2	\frac{d}{dx}(x^{3}-x^{2}-6x+2)
derivative of 2+3(x-1+3(x-1)^2+d(x-1)^3)	\frac{d}{dx}(2+3(x-1)+3(x-1)^{2}+d(x-1)^{3})
derivative of 1/(x+2-1)	\frac{d}{dx}(\frac{1}{x+2}-1)
derivative of 1/(log_{4(x)})	\frac{d}{dx}(\frac{1}{\log_{4}(x)})
integral from 0 to x of sin(t^2)	\int\:_{0}^{x}\sin(t^{2})dt
derivative of-2x^2-1/2 x+10	\frac{d}{dx}(-2x^{2}-\frac{1}{2}x+10)
y^'+(1+1/t)y=1	y^{\prime\:}+(1+\frac{1}{t})y=1
derivative of y=sqrt(6+5x)	derivative\:y=\sqrt{6+5x}
limit as x approaches 8 of x^2	\lim\:_{x\to\:8}(x^{2})
derivative of (cos(x)/(csc(x)))	\frac{d}{dx}(\frac{\cos(x)}{\csc(x)})
(\partial)/(\partial x)(8x^2+y^2)	\frac{\partial\:}{\partial\:x}(8x^{2}+y^{2})
(\partial)/(\partial x)(e^{4xyz-7})	\frac{\partial\:}{\partial\:x}(e^{4xyz-7})
area y=3ln(x),y=0,x=2e	area\:y=3\ln(x),y=0,x=2e
x^2y^'+2xy=sin(4x)	x^{2}y^{\prime\:}+2xy=\sin(4x)
integral of-2xsqrt(9-x^2)	\int\:-2x\sqrt{9-x^{2}}dx
integral of (1+4p)/(2-2p-4p^2)	\int\:\frac{1+4p}{2-2p-4p^{2}}dp
integral from 0 to 4 of (1/4 x+(x+1))	\int\:_{0}^{4}(\frac{1}{4}x+(x+1))dx
derivative of e^{-a/x}	\frac{d}{dx}(e^{-\frac{a}{x}})
limit as x approaches 3 of (4x-12)/(x-3)	\lim\:_{x\to\:3}(\frac{4x-12}{x-3})
integral of (sin(x))/x	\int\:\frac{\sin(x)}{x}dx
integral of (x^2+2)/x	\int\:\frac{x^{2}+2}{x}dx
integral of tan^3(7pix)	\int\:\tan^{3}(7πx)dx
inverse oflaplace (0.5s)/(5s^2+10s+49)	inverselaplace\:\frac{0.5s}{5s^{2}+10s+49}
sum from n=1 to infinity of 1/(e^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{e^{n}}
integral of (x^2-8)/(8x)	\int\:\frac{x^{2}-8}{8x}dx
derivative of ln(arctan(9x^4))	\frac{d}{dx}(\ln(\arctan(9x^{4})))
taylor f(x)=ln(x)	taylor\:f(x)=\ln(x)
limit as x approaches 0 of xln(3x)	\lim\:_{x\to\:0}(x\ln(3x))
limit as k approaches 0 of ((2z+3k)^3-4k^2z)/(2z(2z-k)^2)	\lim\:_{k\to\:0}(\frac{(2z+3k)^{3}-4k^{2}z}{2z(2z-k)^{2}})
integral from 2 to infinity of 2/(x^2-x)	\int\:_{2}^{\infty\:}\frac{2}{x^{2}-x}dx

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