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Popular Calculus Problems

integral from 1 to 3 of (x-1)	\int\:_{1}^{3}(x-1)dx
derivative of 2tan(xsec^2(x))	\frac{d}{dx}(2\tan(x)\sec^{2}(x))
derivative of ln(tan(x))	derivative\:\ln(\tan(x))
(\partial)/(\partial x)(((-x+y))/(xy+3x))	\frac{\partial\:}{\partial\:x}(\frac{(-x+y)}{x\cdot\:y+3\cdot\:x})
y^'=y^2(5+x)	y^{\prime\:}=y^{2}(5+x)
(\partial)/(\partial x)(z/(1+z^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{z}{1+z^{2}y^{2}})
derivative of Axe^{3x}	\frac{d}{dx}(Axe^{3x})
f(t)=sin(t)-tcos(t)	f(t)=\sin(t)-t\cos(t)
f^'(x)=(1-e^x)/(9+e^x)	f^{\prime\:}(x)=\frac{1-e^{x}}{9+e^{x}}
xy^'+y=-2xy^2,y(1)=2	xy^{\prime\:}+y=-2xy^{2},y(1)=2
(\partial)/(\partial y)(y^2sin(xy))	\frac{\partial\:}{\partial\:y}(y^{2}\sin(xy))
limit as x approaches 5 of 2/((x-5)^6)	\lim\:_{x\to\:5}(\frac{2}{(x-5)^{6}})
limit as x approaches 1 of 2x^{-1}	\lim\:_{x\to\:1}(2x^{-1})
laplacetransform te^{-5t}sin(5t)	laplacetransform\:te^{-5t}\sin(5t)
integral of 6e^7	\int\:6e^{7}dx
derivative of e^{2x}+3	\frac{d}{dx}(e^{2x}+3)
y^{''}+5y^'+6y=e-3x	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=e-3x
integral of (e^{2t})/(e^t+3)	\int\:\frac{e^{2t}}{e^{t}+3}dt
(dy)/(dx)+6y=4	\frac{dy}{dx}+6y=4
laplacetransform 2cos(2t)	laplacetransform\:2\cos(2t)
derivative of e^{y-1}	derivative\:e^{y-1}
limit as x approaches 2-of (\|x-2\|)/x	\lim\:_{x\to\:2-}(\frac{\left\|x-2\right\|}{x})
(dy}{dx}=x+\frac{3y)/x	\frac{dy}{dx}=x+\frac{3y}{x}
(\partial)/(\partial x)(1/y-1/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{y}-\frac{1}{x^{2}})
(\partial)/(\partial y)(5x^2y^2)	\frac{\partial\:}{\partial\:y}(5x^{2}y^{2})
xdy-(2xe^{(-y)/x}+y)dx=0	xdy-(2xe^{\frac{-y}{x}}+y)dx=0
d/(dθ)(8cos(θ)+2sin(θ))	\frac{d}{dθ}(8\cos(θ)+2\sin(θ))
(dy)/(dx)-xe^y=2e^y	\frac{dy}{dx}-xe^{y}=2e^{y}
(d^2y)/(dx^2)+2(dy)/(dx)+y=e^{-x}*ln(x)	\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+y=e^{-x}\cdot\:\ln(x)
(\partial)/(\partial x)(1+xy^2)	\frac{\partial\:}{\partial\:x}(1+xy^{2})
limit as h approaches 0 of 3/h	\lim\:_{h\to\:0}(\frac{3}{h})
derivative of 4tan^2(7x)	derivative\:4\tan^{2}(7x)
(dy)/(dx)=-1/2 y	\frac{dy}{dx}=-\frac{1}{2}y
derivative of f(x)=((x^2-1))/(x^2+1)	derivative\:f(x)=\frac{(x^{2}-1)}{x^{2}+1}
integral of 5x^2+(2/x)^4	\int\:5x^{2}+(\frac{2}{x})^{4}dx
(d^2y)/(dx^2)+y=0	\frac{d^{2}y}{dx^{2}}+y=0
y^'-1/x y=x^2e^x	y^{\prime\:}-\frac{1}{x}y=x^{2}e^{x}
derivative of (cos(2x)/(sin(3x)))	\frac{d}{dx}(\frac{\cos(2x)}{\sin(3x)})
integral from 0 to 16 of sqrt(t^2+2t+1)	\int\:_{0}^{16}\sqrt{t^{2}+2t+1}dt
y^'=((x^3y^3+4x^3))/(y^2)	y^{\prime\:}=\frac{(x^{3}y^{3}+4x^{3})}{y^{2}}
integral from 1/5 to 3 of 12xln(5x)	\int\:_{\frac{1}{5}}^{3}12x\ln(5x)dx
integral of (x^2+sqrt(x)+1/x)	\int\:(x^{2}+\sqrt{x}+\frac{1}{x})dx
derivative of f(x)=5x^2-5x+9	derivative\:f(x)=5x^{2}-5x+9
derivative of-9x^3+27x+7x-66	\frac{d}{dx}(-9x^{3}+27x+7x-66)
tangent of 3sqrt(x),\at x=4	tangent\:3\sqrt{x},\at\:x=4
integral of 5tan^3(x)sec^3(x)	\int\:5\tan^{3}(x)\sec^{3}(x)dx
integral from 1 to 4 of 1/(sqrt(x))	\int\:_{1}^{4}\frac{1}{\sqrt{x}}dx
(\partial)/(\partial x)(arcsin(xyz))	\frac{\partial\:}{\partial\:x}(\arcsin(xyz))
integral of (x^3)/((5-x^4)^6)	\int\:\frac{x^{3}}{(5-x^{4})^{6}}dx
(dy)/(dx)=-xy	\frac{dy}{dx}=-xy
integral from 0 to 2pi of cos^2(6x)	\int\:_{0}^{2π}\cos^{2}(6x)dx
(\partial)/(\partial x)(2x^3+3y^2-6xy+2)	\frac{\partial\:}{\partial\:x}(2x^{3}+3y^{2}-6xy+2)
derivative of (2x^4-x+1(-x^5+4))	\frac{d}{dx}((2x^{4}-x+1)(-x^{5}+4))
integral of 5x^9	\int\:5x^{9}dx
derivative of 4t^{1/2}	derivative\:4t^{\frac{1}{2}}
area 4-x^2,2-x	area\:4-x^{2},2-x
derivative of 16xe^{-x}	\frac{d}{dx}(16xe^{-x})
integral of-3x^{-4}	\int\:-3x^{-4}dx
limit as x approaches 1+of sqrt(x^2-1)	\lim\:_{x\to\:1+}(\sqrt{x^{2}-1})
integral from 0 to 1 of 2x(1-x)	\int\:_{0}^{1}2x(1-x)dx
derivative of 2tan^3(x)	derivative\:2\tan^{3}(x)
(\partial)/(\partial x)(6xy+5x^2)	\frac{\partial\:}{\partial\:x}(6xy+5x^{2})
integral of (2x^3-2)/((x^4-4x))	\int\:\frac{2x^{3}-2}{(x^{4}-4x)}dx
integral of (sec(x)-cot(x))^2	\int\:(\sec(x)-\cot(x))^{2}dx
derivative of (x^9+7)/(x^9)	derivative\:\frac{x^{9}+7}{x^{9}}
derivative of 10^{(x^2-1})	\frac{d}{dx}(10^{(x^{2}-1)})
integral of (15e^{5x})/(e^{5x)+2}	\int\:\frac{15e^{5x}}{e^{5x}+2}dx
tangent of f(x)=-4x^2+7x-14,\at x=-2	tangent\:f(x)=-4x^{2}+7x-14,\at\:x=-2
(\partial)/(\partial x)(x^{cos(x)})	\frac{\partial\:}{\partial\:x}(x^{\cos(x)})
derivative of e^{18x}	derivative\:e^{18x}
limit as x approaches infinity of x^{(1/(x^2-1))}	\lim\:_{x\to\:\infty\:}(x^{(\frac{1}{x^{2}-1})})
integral of (x^2-1)^4	\int\:(x^{2}-1)^{4}dx
derivative of ((x+2)/((x-1)))	\frac{d}{dx}(\frac{(x+2)}{(x-1)})
derivative of x^{12}	derivative\:x^{12}
integral of sin^4(5x)cos^6(5x)	\int\:\sin^{4}(5x)\cos^{6}(5x)dx
derivative of-5x^{-6}	\frac{d}{dx}(-5x^{-6})
integral of 11tan^3(x)sec(x)	\int\:11\tan^{3}(x)\sec(x)dx
derivative of (sin(5x)^{ln(x)})	\frac{d}{dx}((\sin(5x))^{\ln(x)})
derivative of (81/(x^4))	\frac{d}{dx}(\frac{81}{x^{4}})
y^'-y/x =tan(y/x)	y^{\prime\:}-\frac{y}{x}=\tan(\frac{y}{x})
integral of x/((x^2+4x+5)^{3/2)}	\int\:\frac{x}{(x^{2}+4x+5)^{\frac{3}{2}}}dx
(dy)/(dx)=((x-4))/((y+5))	\frac{dy}{dx}=\frac{(x-4)}{(y+5)}
derivative of ax^2+bx+c	derivative\:ax^{2}+bx+c
derivative of (6x/(1-tan(x)))	\frac{d}{dx}(\frac{6x}{1-\tan(x)})
integral from 0 to pi/4 of 6sec^2(x)	\int\:_{0}^{\frac{π}{4}}6\sec^{2}(x)dx
integral of (sqrt(y^5-1))/y	\int\:\frac{\sqrt{y^{5}-1}}{y}dy
derivative of 1+3^{sin(x^3})	\frac{d}{dx}(1+3^{\sin(x^{3})})
derivative of (x^3+2x+6)(4+1/(x^2))	derivative\:(x^{3}+2x+6)(4+\frac{1}{x^{2}})
integral of x^2csc(x^3)cot(x^3)	\int\:x^{2}\csc(x^{3})\cot(x^{3})dx
derivative of f(x)=-4x^2-3x	derivative\:f(x)=-4x^{2}-3x
(\partial)/(\partial x)(sqrt(x^2+y^2)+1)	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}}+1)
derivative of f(x)= x/((x-7)^2)	derivative\:f(x)=\frac{x}{(x-7)^{2}}
f(x)=((e^x+e^{-x}))/2	f(x)=\frac{(e^{x}+e^{-x})}{2}
limit as x approaches 0 of x/(x+\|x\|)	\lim\:_{x\to\:0}(\frac{x}{x+\left\|x\right\|})
area y= 1/(18x^2),y=x,y= x/(10)	area\:y=\frac{1}{18x^{2}},y=x,y=\frac{x}{10}
integral of (x-4)/(x^2)	\int\:\frac{x-4}{x^{2}}dx
derivative of f(x)=6e^x(cos(x)-sin(x))	derivative\:f(x)=6e^{x}(\cos(x)-\sin(x))
derivative of 3t^7+4t^5-sqrt(t)	derivative\:3t^{7}+4t^{5}-\sqrt{t}
derivative of ln((4x^2-9/(2x-3)))	\frac{d}{dx}(\ln(\frac{4x^{2}-9}{2x-3}))
limit as x approaches 1+of sqrt(x^2-x)	\lim\:_{x\to\:1+}(\sqrt{x^{2}-x})

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