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Popular Calculus Problems

derivative of x/(x^2+169)	\frac{d}{dx}(\frac{x}{x^{2}+169})
derivative of y=x^{x^3}	derivative\:y=x^{x^{3}}
integral of (4x^2+4x)/(2x-1)	\int\:\frac{4x^{2}+4x}{2x-1}dx
integral of 1/(sqrt(-x^2-4x+21))	\int\:\frac{1}{\sqrt{-x^{2}-4x+21}}dx
integral of (2e^x)/(sqrt(1-e^{2x))}	\int\:\frac{2e^{x}}{\sqrt{1-e^{2x}}}dx
derivative of 9x^2sin(x)tan(x)	derivative\:9x^{2}\sin(x)\tan(x)
integral of acos(t)	\int\:a\cos(t)dt
(dy)/(dx)=(5(3-y)^2)/((3-x)^2)	\frac{dy}{dx}=\frac{5(3-y)^{2}}{(3-x)^{2}}
derivative of 7/10 x^2+4^3	\frac{d}{dx}(\frac{7}{10}x^{2}+4^{3})
(dy)/(dx)=(18(2+y)^2)/((1-3x)^2)	\frac{dy}{dx}=\frac{18(2+y)^{2}}{(1-3x)^{2}}
integral of (x^2-2x+3)ln(x)	\int\:(x^{2}-2x+3)\ln(x)dx
limit as x approaches 0 of 3(x^{x/2})	\lim\:_{x\to\:0}(3(x^{\frac{x}{2}}))
tangent of f(x)= 6/(5x+3),\at x=-1	tangent\:f(x)=\frac{6}{5x+3},\at\:x=-1
x^'=x+1	x^{\prime\:}=x+1
extreme f(x)=9xe^{-kx}	extreme\:f(x)=9xe^{-kx}
simplify-x^{-3}	simplify\:-x^{-3}
(\partial)/(\partial z)(sqrt(y-x)-z)	\frac{\partial\:}{\partial\:z}(\sqrt{y-x}-z)
derivative of-3x^{1/2}	\frac{d}{dx}(-3x^{\frac{1}{2}})
integral of (3x)/(x^2-1)	\int\:\frac{3x}{x^{2}-1}dx
integral of 2xsqrt(x+2)	\int\:2x\sqrt{x+2}dx
y^{''}-22y^'+121y=0	y^{\prime\:\prime\:}-22y^{\prime\:}+121y=0
limit as n approaches infinity of \sum_{i=1}^n 1/(2n+i)	\lim\:_{n\to\:\infty\:}(\sum\:_{i=1}^{n}\frac{1}{2n+i})
(\partial)/(\partial x)(5x^2y^3+2x^2+7y)	\frac{\partial\:}{\partial\:x}(5x^{2}y^{3}+2x^{2}+7y)
maclaurin f(x)=e^{-x},5	maclaurin\:f(x)=e^{-x},5
derivative of y=ln(sqrt(5x)*(2x^3-4x)^5)	derivative\:y=\ln(\sqrt{5x}\cdot\:(2x^{3}-4x)^{5})
integral of 1+e^xsin(y)	\int\:1+e^{x}\sin(y)dx
(dy)/(dx)=((x+3y))/((y-3x))	\frac{dy}{dx}=\frac{(x+3y)}{(y-3x)}
y^'=3x	y^{\prime\:}=3x
derivative of e^{-2*x}	\frac{d}{dx}(e^{-2\cdot\:x})
derivative of x^3+e^x	derivative\:x^{3}+e^{x}
integral of sqrt(9+t^2)	\int\:\sqrt{9+t^{2}}dt
(dy)/(dx)= y/x+(9x^2)/(y^2)	\frac{dy}{dx}=\frac{y}{x}+\frac{9x^{2}}{y^{2}}
integral of (12x^2)/(4x^3+1)	\int\:\frac{12x^{2}}{4x^{3}+1}dx
integral of (2x-5)/(x^2-5x+6)	\int\:\frac{2x-5}{x^{2}-5x+6}dx
integral from 12 to infinity of xe^{-x}	\int\:_{12}^{\infty\:}xe^{-x}dx
f(x)=sin(e^x)	f(x)=\sin(e^{x})
derivative of sqrt(f(x))	derivative\:\sqrt{f(x)}
integral of 1/(x+x^3)	\int\:\frac{1}{x+x^{3}}dx
(\partial}{\partial x}(e^{-\frac{x^2)/6-(y^2)/6})	\frac{\partial\:}{\partial\:x}(e^{-\frac{x^{2}}{6}-\frac{y^{2}}{6}})
integral of ((5x^4)/((10+x^5)^4))	\int\:(\frac{5x^{4}}{(10+x^{5})^{4}})dx
sum from n=1 to infinity of (cos(1.6))^n	\sum\:_{n=1}^{\infty\:}(\cos(1.6))^{n}
integral of arcsin(2x)	\int\:\arcsin(2x)dx
(\partial)/(\partial y)(e^y+e^{2xy})	\frac{\partial\:}{\partial\:y}(e^{y}+e^{2xy})
limit as x approaches 0-of (\|8x\|)/x	\lim\:_{x\to\:0-}(\frac{\left\|8x\right\|}{x})
derivative of x*e^{-bx^2}	\frac{d}{dx}(x\cdot\:e^{-bx^{2}})
derivative of 7e^{sqrt(x)}	derivative\:7e^{\sqrt{x}}
inverse oflaplace (12(s+2))/(s(s^2+9))	inverselaplace\:\frac{12(s+2)}{s(s^{2}+9)}
integral from 0 to 36 of 1/(sqrt(36-x))	\int\:_{0}^{36}\frac{1}{\sqrt{36-x}}dx
area y=5x,x=5,y= 5/x	area\:y=5x,x=5,y=\frac{5}{x}
derivative of x^3+tan(sin(x)+2)	\frac{d}{dx}(x^{3}+\tan(\sin(x))+2)
derivative of-x^2+1.8x+2.5	\frac{d}{dx}(-x^{2}+1.8x+2.5)
y^{''}-y=0,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}-y=0,y(0)=1,y^{\prime\:}(0)=1
limit as x approaches 0-of ln\|e^x-1\|	\lim\:_{x\to\:0-}(\ln\left\|e^{x}-1\right\|)
derivative of 3x+x^{1/2}	\frac{d}{dx}(3x+x^{\frac{1}{2}})
tangent of y=(x-4)(x^2+8),(1,-27)	tangent\:y=(x-4)(x^{2}+8),(1,-27)
derivative of e^x-1+e^xx	\frac{d}{dx}(e^{x}-1+e^{x}x)
(\partial)/(\partial x)(x^{0.2}y^{0.8})	\frac{\partial\:}{\partial\:x}(x^{0.2}y^{0.8})
integral of (4x+3)(2x^2+3)^3	\int\:(4x+3)(2x^{2}+3)^{3}dx
(\partial)/(\partial z)(x^2y^3z)	\frac{\partial\:}{\partial\:z}(x^{2}y^{3}z)
derivative of 1/(sqrt(2+x))	\frac{d}{dx}(\frac{1}{\sqrt{2+x}})
(dy)/(dx)=2-(2x)/(1000-x)	\frac{dy}{dx}=2-\frac{2x}{1000-x}
derivative of xcoth(1+x^2)	\frac{d}{dx}(x\coth(1+x^{2}))
derivative of y=ln(1+e^x)	derivative\:y=\ln(1+e^{x})
(\partial)/(\partial x)(sin(5x-8y))	\frac{\partial\:}{\partial\:x}(\sin(5x-8y))
area e^x,e^{-3x},x=ln(3)	area\:e^{x},e^{-3x},x=\ln(3)
integral of (9x+6)/((x-6)(x+4))	\int\:\frac{9x+6}{(x-6)(x+4)}dx
integral from 1 to 2 of (x+1)/(x(x^2+1))	\int\:_{1}^{2}\frac{x+1}{x(x^{2}+1)}dx
derivative of y=ln(sqrt(x^2+4))	derivative\:y=\ln(\sqrt{x^{2}+4})
limit as x approaches 6 of x	\lim\:_{x\to\:6}(x)
integral from 0 to \sqrt[3]{pi^2 of}sqrt(θ)cos^2(θ^{3/2})	\int\:_{0}^{\sqrt[3]{π^{2}}}\sqrt{θ}\cos^{2}(θ^{\frac{3}{2}})dθ
(\partial)/(\partial x)(2/x-x)	\frac{\partial\:}{\partial\:x}(\frac{2}{x}-x)
derivative of-8e^{-2x}	\frac{d}{dx}(-8e^{-2x})
limit as x approaches 4 of 2*e^{2/(x-4)}	\lim\:_{x\to\:4}(2\cdot\:e^{\frac{2}{x-4}})
limit as x approaches 0 of (-3)sin(7x)	\lim\:_{x\to\:0}((-3)\sin(7x))
y^{''}-1=0	y^{\prime\:\prime\:}-1=0
integral of ln\|x\|*1	\int\:\ln\left\|x\right\|\cdot\:1dx
integral of sin(10x)sin(15x)	\int\:\sin(10x)\sin(15x)dx
derivative of (ln(x)/(x^{11)})	\frac{d}{dx}(\frac{\ln(x)}{x^{11}})
partialfraction (x^3)/(x^2-1)	partialfraction\:\frac{x^{3}}{x^{2}-1}
sum from k=1 to infinity of 0.5^k	\sum\:_{k=1}^{\infty\:}0.5^{k}
integral of 1/4096 cos(8x)	\int\:\frac{1}{4096}\cos(8x)dx
integral of 1+\sqrt[3]{x-1}	\int\:1+\sqrt[3]{x-1}dx
inverse oflaplace (e^{-2s})/(s-1)	inverselaplace\:\frac{e^{-2s}}{s-1}
(dy)/(dt)= 2/t y+t^3e^t	\frac{dy}{dt}=\frac{2}{t}y+t^{3}e^{t}
integral of 3^{-6x}	\int\:3^{-6x}dx
inverse oflaplace 3/(s(s^2+2s+4))	inverselaplace\:\frac{3}{s(s^{2}+2s+4)}
integral of y^{-5}	\int\:y^{-5}dy
y^'=y^2cos(x)	y^{\prime\:}=y^{2}\cos(x)
limit as x approaches-1 of (x+2x^5)^3	\lim\:_{x\to\:-1}((x+2x^{5})^{3})
integral of (e^x-e^5)(e^x+e^{-3})	\int\:(e^{x}-e^{5})(e^{x}+e^{-3})dx
area x=7y^2,x=2+5y^2	area\:x=7y^{2},x=2+5y^{2}
integral of 200e^{0.02x}	\int\:200e^{0.02x}dx
integral of (x^2)/(sqrt(16-x^6))	\int\:\frac{x^{2}}{\sqrt{16-x^{6}}}dx
derivative of xsec^2(x)	\frac{d}{dx}(x\sec^{2}(x))
y^'=(x^3+y^3)/(xy^2)	y^{\prime\:}=\frac{x^{3}+y^{3}}{xy^{2}}
(dy)/(dx)y=11x	\frac{dy}{dx}y=11x
tangent of f(x)=-x^4+4x^3+8x^2+5,\at x=2	tangent\:f(x)=-x^{4}+4x^{3}+8x^{2}+5,\at\:x=2
d/(dt)(t^2+3t-2)	\frac{d}{dt}(t^{2}+3t-2)
(\partial)/(\partial x)(7e^{8x})	\frac{\partial\:}{\partial\:x}(7e^{8x})
(\partial)/(\partial x)(e^{xyz^4})	\frac{\partial\:}{\partial\:x}(e^{xyz^{4}})

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