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Popular Calculus Problems

derivative of f(x)=sqrt(2-x^2)	derivative\:f(x)=\sqrt{2-x^{2}}
tangent of f(x)=5+5x^2-2x^3,\at x=a	tangent\:f(x)=5+5x^{2}-2x^{3},\at\:x=a
limit as x approaches 0 of 3/(1+x)	\lim\:_{x\to\:0}(\frac{3}{1+x})
derivative of x+sin^2(x)	\frac{d}{dx}(x+\sin^{2}(x))
(2xy+x^2+x^4)dx-(1+x^2)dy=0	(2xy+x^{2}+x^{4})dx-(1+x^{2})dy=0
(\partial)/(\partial x)(x^{(y/z)})	\frac{\partial\:}{\partial\:x}(x^{(\frac{y}{z})})
derivative of 35.4cos(0.1(x+6.2))	derivative\:35.4\cos(0.1(x+6.2))
limit as x approaches 1.01 of 1/(x^2-1)	\lim\:_{x\to\:1.01}(\frac{1}{x^{2}-1})
derivative of 1+3x+9x^2	\frac{d}{dx}(1+3x+9x^{2})
derivative of f(x)=5x^2	derivative\:f(x)=5x^{2}
(9x^2+y-1)dx-(14y-x)dy=0,y(1)=0	(9x^{2}+y-1)dx-(14y-x)dy=0,y(1)=0
integral from 0 to 1 of (x+sqrt(1-x^2))	\int\:_{0}^{1}(x+\sqrt{1-x^{2}})dx
integral of 10^x(2^{-x}+5^{-x})	\int\:10^{x}(2^{-x}+5^{-x})dx
derivative of Ax^2e^{2x}	\frac{d}{dx}(Ax^{2}e^{2x})
integral of e^x-x^{2/5}	\int\:e^{x}-x^{\frac{2}{5}}dx
inverse oflaplace 3/(2s+1)*1/s	inverselaplace\:\frac{3}{2s+1}\cdot\:\frac{1}{s}
derivative of (x-1/x ^2)	\frac{d}{dx}((x-\frac{1}{x})^{2})
limit as t approaches x/2 of (sin(t))/t	\lim\:_{t\to\:\frac{x}{2}}(\frac{\sin(t)}{t})
slope of (-3.5)(4.3)	slope\:(-3.5)(4.3)
(\partial)/(\partial x)(-x/(y^2))	\frac{\partial\:}{\partial\:x}(-\frac{x}{y^{2}})
inverse oflaplace (s+2)/(s^2+2s+2)	inverselaplace\:\frac{s+2}{s^{2}+2s+2}
limit as x approaches-4 of 7-x	\lim\:_{x\to\:-4}(7-x)
integral from-2 to 2 of x^3cos(x/2)	\int\:_{-2}^{2}x^{3}\cos(\frac{x}{2})dx
integral from 0 to 1 of e^{-0.2x}	\int\:_{0}^{1}e^{-0.2x}dx
limit as x approaches infinity+of cos(x)	\lim\:_{x\to\:\infty\:+}(\cos(x))
integral from 1 to 2 of xln(4x)	\int\:_{1}^{2}x\ln(4x)dx
integral of 12sin^2(x)cos^2(x)	\int\:12\sin^{2}(x)\cos^{2}(x)dx
derivative of cos(x)x^3	derivative\:\cos(x)x^{3}
integral from-pi to pi of cos(nx)cos(mx)	\int\:_{-π}^{π}\cos(nx)\cos(mx)dx
y^{''}-12y^'+36y=te^{6t}	y^{\prime\:\prime\:}-12y^{\prime\:}+36y=te^{6t}
integral of sin((npix)/4)	\int\:\sin(\frac{nπx}{4})dx
derivative of (2+sin(x)/(2x+cos(x)))	\frac{d}{dx}(\frac{2+\sin(x)}{2x+\cos(x)})
area y=\|x\|,y=x^2-1,x=-1,x=1	area\:y=\left\|x\right\|,y=x^{2}-1,x=-1,x=1
5t(dy)/(dt)-5y=sqrt(t)	5t\frac{dy}{dt}-5y=\sqrt{t}
(\partial)/(\partial y)(y/(sqrt(x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{y}{\sqrt{x^{2}+y^{2}}})
(\partial)/(\partial x)(x^3z+yz)	\frac{\partial\:}{\partial\:x}(x^{3}z+yz)
derivative of 1/((2x+1^2))	\frac{d}{dx}(\frac{1}{(2x+1)^{2}})
derivative of 8/(2x)	\frac{d}{dx}(\frac{8}{2x})
(\partial)/(\partial y)(e^{cos(x-2y)})	\frac{\partial\:}{\partial\:y}(e^{\cos(x-2y)})
derivative of ln(1-8x)	\frac{d}{dx}(\ln(1-8x))
derivative of y=\sqrt[3]{x^2}	derivative\:y=\sqrt[3]{x^{2}}
derivative of 6ln(\sqrt[3]{x})	\frac{d}{dx}(6\ln(\sqrt[3]{x}))
x(dy)/(dx)-y=3x^4	x\frac{dy}{dx}-y=3x^{4}
derivative of (-3x+1^3(2x-1)^4)	\frac{d}{dx}((-3x+1)^{3}(2x-1)^{4})
derivative of 1/((x^2+3x+2^3))	\frac{d}{dx}(\frac{1}{(x^{2}+3x+2)^{3}})
integral of cosh(x	\int\:\cosh(d)xdx
(\partial)/(\partial x)(x^2y-x)	\frac{\partial\:}{\partial\:x}(x^{2}y-x)
integral of tan(x^2)	\int\:\tan(x^{2})dx
laplacetransform 0.0796-0.066*x^{1/2}	laplacetransform\:0.0796-0.066\cdot\:x^{\frac{1}{2}}
integral from 0 to 1 of 3(1+sqrt(x))^5	\int\:_{0}^{1}3(1+\sqrt{x})^{5}dx
integral from 0 to 1 of (2x-3)	\int\:_{0}^{1}(2x-3)dx
(dy)/(dx)=-10y	\frac{dy}{dx}=-10y
derivative of f(x)=(x^3+2x+7)/(x^2-5)	derivative\:f(x)=\frac{x^{3}+2x+7}{x^{2}-5}
integral from 1 to 1.5 of 2/5 (x+1)	\int\:_{1}^{1.5}\frac{2}{5}(x+1)dx
derivative of f(t)=6t^3-54t^2+70	derivative\:f(t)=6t^{3}-54t^{2}+70
derivative of 1/(\sqrt[3]{x^3+1})	\frac{d}{dx}(\frac{1}{\sqrt[3]{x^{3}+1}})
(10-6y+e^{-3x})dx-2dy=0	(10-6y+e^{-3x})dx-2dy=0
derivative of (x^2+1/(x^2+x+1))	\frac{d}{dx}(\frac{x^{2}+1}{x^{2}+x+1})
integral of arcsin(sqrt(x/(x+1)))	\int\:\arcsin(\sqrt{\frac{x}{x+1}})dx
(\partial)/(\partial x)(e^{-1/2 xy})	\frac{\partial\:}{\partial\:x}(e^{-\frac{1}{2}xy})
integral of-2x+6	\int\:-2x+6dx
y^'+1/(x+7)y=x^{-2},y(1)=4	y^{\prime\:}+\frac{1}{x+7}y=x^{-2},y(1)=4
integral of \sqrt[6]{x^7}	\int\:\sqrt[6]{x^{7}}dx
(\partial)/(\partial x)(xcos(x)cos(y))	\frac{\partial\:}{\partial\:x}(x\cos(x)\cos(y))
limit as x approaches 2 of (3x^2-5x-2)/(2x-1)	\lim\:_{x\to\:2}(\frac{3x^{2}-5x-2}{2x-1})
y^2dx=(2xy+x^2)dy	y^{2}dx=(2xy+x^{2})dy
integral of 4e^{-5x}	\int\:4e^{-5x}dx
integral of (1-cos(x))^2	\int\:(1-\cos(x))^{2}dx
laplacetransform 4-4*e^{2t}	laplacetransform\:4-4\cdot\:e^{2t}
derivative of f(x)=(e^x)/(x^2+1)	derivative\:f(x)=\frac{e^{x}}{x^{2}+1}
integral of (7x^2)e^{x^3+1}	\int\:(7x^{2})e^{x^{3}+1}dx
integral of e^{-2y}y	\int\:e^{-2y}ydy
tangent of f(x)=-x^3+x^2+4x-2,\at x=0	tangent\:f(x)=-x^{3}+x^{2}+4x-2,\at\:x=0
(\partial)/(\partial y)(ye^{xy}sin(y))	\frac{\partial\:}{\partial\:y}(ye^{xy}\sin(y))
limit as x approaches 2-of 3x	\lim\:_{x\to\:2-}(3x)
limit as x approaches 0+of x^3cot(x)	\lim\:_{x\to\:0+}(x^{3}\cot(x))
5x^{''}+50x-10=0	5x^{\prime\:\prime\:}+50x-10=0
(\partial)/(\partial y)((2x+3y)^7)	\frac{\partial\:}{\partial\:y}((2x+3y)^{7})
d/(du)(ln(ucos(v)))	\frac{d}{du}(\ln(u\cos(v)))
(dy)/(dx)=xy,y(0)=2	\frac{dy}{dx}=xy,y(0)=2
derivative of f(x)=2e^{2x-4}-e^{2x-4}	derivative\:f(x)=2e^{2x-4}-e^{2x-4}
integral from 0 to 5 of 2piy(25-y^2)	\int\:_{0}^{5}2πy(25-y^{2})dy
(cos(ln(x)))^'	(\cos(\ln(x)))^{\prime\:}
derivative of a{r}(xc)	\frac{d}{dx}(a{r}(x)c)
derivative of 2sin(x)+sin^2(x)	derivative\:2\sin(x)+\sin^{2}(x)
(\partial)/(\partial t)(y+xcos(t))	\frac{\partial\:}{\partial\:t}(y+x\cos(t))
integral of 9x^2	\int\:9x^{2}dx
y^{''}+14y^'+50y=0,y(0)=2,y^'(0)=-17	y^{\prime\:\prime\:}+14y^{\prime\:}+50y=0,y(0)=2,y^{\prime\:}(0)=-17
derivative of y=(2tan^2(2x)-1)^{1/2}	derivative\:y=(2\tan^{2}(2x)-1)^{\frac{1}{2}}
(\partial)/(\partial x)(x(1-x-2y))	\frac{\partial\:}{\partial\:x}(x(1-x-2y))
y'=0.002y(2500-y)	y\prime\:=0.002y(2500-y)
(d^2)/(dx^2)(x^3+y^3)	\frac{d^{2}}{dx^{2}}(x^{3}+y^{3})
derivative of pi^2	derivative\:π^{2}
integral of 2/(3x-2)	\int\:\frac{2}{3x-2}dx
derivative of (sec(2x)^7)	\frac{d}{dx}((\sec(2x))^{7})
area 5-x^2,2-2x	area\:5-x^{2},2-2x
integral of (x^2+x)^{11}(2x+1)	\int\:(x^{2}+x)^{11}(2x+1)dx
integral of (xe^{3x})/3	\int\:\frac{xe^{3x}}{3}dx
integral of xsin(x)+cos(x)+c	\int\:x\sin(x)+\cos(x)+cdx
derivative of-3cos(x+xsin(x))	\frac{d}{dx}(-3\cos(x)+x\sin(x))

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