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Popular Calculus Problems

derivative of (1-x^{-1}^{-1})	\frac{d}{dx}((1-x^{-1})^{-1})
y^'=((4+5*y))/6	y^{\prime\:}=\frac{(4+5\cdot\:y)}{6}
integral of x*x^{1/2}	\int\:x\cdot\:x^{\frac{1}{2}}dx
limit as x approaches 0 of (x^2)*ln(x)	\lim\:_{x\to\:0}((x^{2})\cdot\:\ln(x))
y^'+1/x y=0	y^{\prime\:}+\frac{1}{x}y=0
tangent of f(x)=3x^3-3x^2+7,(2,19)	tangent\:f(x)=3x^{3}-3x^{2}+7,(2,19)
derivative of 3^xlog_{5}(x)	\frac{d}{dx}(3^{x}\log_{5}(x))
integral from 0 to x of 1/(1-x)	\int\:_{0}^{x}\frac{1}{1-x}dx
d/(dθ)(1/θ)	\frac{d}{dθ}(\frac{1}{θ})
(\partial)/(\partial x)(6e^{x^3y})	\frac{\partial\:}{\partial\:x}(6e^{x^{3}y})
integral of sqrt(26)	\int\:\sqrt{26}dx
tangent of f(x)=3x^3-x^2+8,(2,28)	tangent\:f(x)=3x^{3}-x^{2}+8,(2,28)
derivative of sqrt(8-x^2)	\frac{d}{dx}(\sqrt{8-x^{2}})
derivative of y=(sqrt(t))^t	derivative\:y=(\sqrt{t})^{t}
limit as x approaches 1/3 of (x+3)/(x+4)	\lim\:_{x\to\:\frac{1}{3}}(\frac{x+3}{x+4})
derivative of (x^2dx)	\frac{d}{dx}((x^{2})dx)
limit as x approaches-3 of (x^2+x)/(x+3)	\lim\:_{x\to\:-3}(\frac{x^{2}+x}{x+3})
integral of 3y^3e^{xy}	\int\:3y^{3}e^{xy}dx
integral of x^2e^{2x+1}	\int\:x^{2}e^{2x+1}dx
tangent of f(x)=-3x^2-5,\at x=0	tangent\:f(x)=-3x^{2}-5,\at\:x=0
derivative of (x-1/(x-2))	\frac{d}{dx}(\frac{x-1}{x-2})
integral of (tan(θ))/(sec^2(θ))	\int\:\frac{\tan(θ)}{\sec^{2}(θ)}dθ
simplify 8/(sqrt(x))	simplify\:\frac{8}{\sqrt{x}}
derivative of a(1-cos^2(x/2)^2)	\frac{d}{dx}(a(1-\cos^{2}(\frac{x}{2}))^{2})
expand (x-2)(x-7)(x+1)	expand\:(x-2)(x-7)(x+1)
laplacetransform 27t^2sin(6t-60)	laplacetransform\:27t^{2}\sin(6t-60)
(\partial)/(\partial x)(3e^{x/y})	\frac{\partial\:}{\partial\:x}(3e^{\frac{x}{y}})
tangent of y= 6/(sqrt(x)),(1, 6/1)	tangent\:y=\frac{6}{\sqrt{x}},(1,\frac{6}{1})
derivative of (cos(sqrt(x))/x)	\frac{d}{dx}(\frac{\cos(\sqrt{x})}{x})
(2xy^2-3)dx+(2x^2y+4)dy=0	(2xy^{2}-3)dx+(2x^{2}y+4)dy=0
derivative of x/((1+x^2^2))	\frac{d}{dx}(\frac{x}{(1+x^{2})^{2}})
(d^2)/(dx^2)((x^2+8)^9)	\frac{d^{2}}{dx^{2}}((x^{2}+8)^{9})
derivative of ((x^2)/2)	\frac{d}{dx}(\frac{(x^{2})}{2})
tangent of (sqrt(3))^x	tangent\:(\sqrt{3})^{x}
(\partial)/(\partial x)(5ye^x-ln(z))	\frac{\partial\:}{\partial\:x}(5ye^{x}-\ln(z))
integral of 1/(x^4)-1/(\sqrt[4]{x)}-4	\int\:\frac{1}{x^{4}}-\frac{1}{\sqrt[4]{x}}-4dx
derivative of f(x)=sec^2(pix)	derivative\:f(x)=\sec^{2}(πx)
integral of-1/4 x	\int\:-\frac{1}{4}xdx
laplacetransform e^{-2t}cos(3t)	laplacetransform\:e^{-2t}\cos(3t)
(\partial)/(\partial y)(y+1)	\frac{\partial\:}{\partial\:y}(y+1)
inverse oflaplace 6/((s+1)(2s^2+5s+3))	inverselaplace\:\frac{6}{(s+1)(2s^{2}+5s+3)}
integral from 0 to 1 of (x^2)/((x+3)^2)	\int\:_{0}^{1}\frac{x^{2}}{(x+3)^{2}}dx
integral of e^{10x}*5x	\int\:e^{10x}\cdot\:5xdx
area x=4y,x=y^2-5	area\:x=4y,x=y^{2}-5
integral from-4 to 4 of (2x^7+1)	\int\:_{-4}^{4}(2x^{7}+1)dx
derivative of (1/(y^2)-9/(y^4))(y+3y^3)	derivative\:(\frac{1}{y^{2}}-\frac{9}{y^{4}})(y+3y^{3})
integral from 2 to 4 of f(x)	\int\:_{2}^{4}f(x)dx
f^'(x)= 4/x	f^{\prime\:}(x)=\frac{4}{x}
d/(dt)(sin(6t))	\frac{d}{dt}(\sin(6t))
integral of 1/(sqrt(36x^2+2))	\int\:\frac{1}{\sqrt{36x^{2}+2}}dx
integral from 0 to 1/2 of cos^3(pix)	\int\:_{0}^{\frac{1}{2}}\cos^{3}(πx)dx
derivative of (x^4+9x^2-7^8)	\frac{d}{dx}((x^{4}+9x^{2}-7)^{8})
derivative of ln((7x^{ln(2x)}))	\frac{d}{dx}(\ln((7x)^{\ln(2x)}))
(\partial)/(\partial z)(8ze^{xyz})	\frac{\partial\:}{\partial\:z}(8ze^{xyz})
d/(dt)(ccos(t)+t^2sin(t))	\frac{d}{dt}(c\cos(t)+t^{2}\sin(t))
integral of 6/(x^2(x^2+25))	\int\:\frac{6}{x^{2}(x^{2}+25)}dx
limit as x approaches 0 of x^2+x+1	\lim\:_{x\to\:0}(x^{2}+x+1)
derivative of y=x^6f(x)	derivative\:y=x^{6}f(x)
e^{x-y}y^'=x-3	e^{x-y}y^{\prime\:}=x-3
(\partial)/(\partial z)(x^2+y^2z)	\frac{\partial\:}{\partial\:z}(x^{2}+y^{2}z)
laplacetransform-8e^{pi-t}	laplacetransform\:-8e^{π-t}
derivative of (x^3+2x^2)^{-1}	derivative\:(x^{3}+2x^{2})^{-1}
sum from n=1 to infinity of arctan(n+1)	\sum\:_{n=1}^{\infty\:}\arctan(n+1)
limit as z approaches i of z(z+1)	\lim\:_{z\to\:i}(z(z+1))
derivative of f(x)=ln(4x+1)	derivative\:f(x)=\ln(4x+1)
derivative of 1/(ln^2(x))	\frac{d}{dx}(\frac{1}{\ln^{2}(x)})
integral of 1/(xsqrt(9x^2+16))	\int\:\frac{1}{x\sqrt{9x^{2}+16}}dx
integral of t^2sqrt(t^3+1)	\int\:t^{2}\sqrt{t^{3}+1}dt
integral of (r^3)/(sqrt(4+r^2))	\int\:\frac{r^{3}}{\sqrt{4+r^{2}}}dr
limit as x approaches 2-of (1-x)/(x-2)	\lim\:_{x\to\:2-}(\frac{1-x}{x-2})
xy^'-2y=12x^2	xy^{\prime\:}-2y=12x^{2}
derivative of x^2+5x-8	\frac{d}{dx}(x^{2}+5x-8)
-18y^{''}-14y^'=0,y(3)=-3,y^'(3)=-3	-18y^{\prime\:\prime\:}-14y^{\prime\:}=0,y(3)=-3,y^{\prime\:}(3)=-3
integral of (3x)/(sqrt(x^2-11))	\int\:\frac{3x}{\sqrt{x^{2}-11}}dx
integral of (4xe^x+e^{4x})/(e^{3x)}	\int\:\frac{4xe^{x}+e^{4x}}{e^{3x}}dx
integral from 1 to 4 of f(x)	\int\:_{1}^{4}f(x)dx
derivative of x(x^5+1^3)	\frac{d}{dx}(x(x^{5}+1)^{3})
(\partial)/(\partial y)(xe^y-ln(x))	\frac{\partial\:}{\partial\:y}(xe^{y}-\ln(x))
derivative of-x-1/x	derivative\:-x-\frac{1}{x}
limit as x approaches 0 of x^{-1}	\lim\:_{x\to\:0}(x^{-1})
integral from-2 to 3 of (14)/(x^4)	\int\:_{-2}^{3}\frac{14}{x^{4}}dx
derivative of xe^xsin(y)	\frac{d}{dx}(xe^{x}\sin(y))
y^{''}+3y^'-7y=x^4e^x	y^{\prime\:\prime\:}+3y^{\prime\:}-7y=x^{4}e^{x}
area y=x^2-2x+2,y=4	area\:y=x^{2}-2x+2,y=4
limit as x approaches 0 of xcot(1/4 x)	\lim\:_{x\to\:0}(x\cot(\frac{1}{4}x))
x^{''}+2x^'+5x=0	x^{\prime\:\prime\:}+2x^{\prime\:}+5x=0
derivative of (e^x+e^{-x})/(e^x-e^{-x)}	derivative\:\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}
integral of y/(sqrt(16-9y^4))	\int\:\frac{y}{\sqrt{16-9y^{4}}}dy
integral of (2x^3+x)(x^4+x^2)	\int\:(2x^{3}+x)(x^{4}+x^{2})dx
derivative of f(x)=-2x+7	derivative\:f(x)=-2x+7
integral of 7x^9-3x^6+10x^3	\int\:7x^{9}-3x^{6}+10x^{3}dx
integral of 1/((x+1)^5)	\int\:\frac{1}{(x+1)^{5}}dx
limit as x approaches 0 of (e^{bx}-1)/x	\lim\:_{x\to\:0}(\frac{e^{bx}-1}{x})
limit as x approaches+1 of x/((x-1))	\lim\:_{x\to\:+1}(\frac{x}{(x-1)})
limit as x approaches 0 of (x-6)/(x-2)	\lim\:_{x\to\:0}(\frac{x-6}{x-2})
(d^3)/(dx^3)(sqrt(1+x))	\frac{d^{3}}{dx^{3}}(\sqrt{1+x})
(dy)/(dx)=12	\frac{dy}{dx}=12
derivative of x+1/(x+2)	\frac{d}{dx}(x+\frac{1}{x+2})
derivative of f(x)=sqrt(x)(x+3)	derivative\:f(x)=\sqrt{x}(x+3)
derivative of sqrt(6-3x)	\frac{d}{dx}(\sqrt{6-3x})

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