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Popular Calculus Problems

derivative of axcos(x+bcos(x))	\frac{d}{dx}(ax\cos(x)+b\cos(x))
d/(d{x)}(e^{-({x}^2+{y}^2+{z}^2)})	\frac{d}{d{x}}(e^{-({x}^{2}+{y}^{2}+{z}^{2})})
(dy)/(dx)=((x^3+y^3))/(3xy^2)	\frac{dy}{dx}=\frac{(x^{3}+y^{3})}{3\cdot\:x\cdot\:y^{2}}
(dy)/(dx)=(y^2)/(x^3)	\frac{dy}{dx}=\frac{y^{2}}{x^{3}}
integral of 7x^2sqrt(1-x^3)	\int\:7x^{2}\sqrt{1-x^{3}}dx
(dy)/(e^{5y)}=e^{4x}dx	\frac{dy}{e^{5y}}=e^{4x}dx
limit as x approaches infinity of-x^4	\lim\:_{x\to\:\infty\:}(-x^{4})
(dy}{dx}=\frac{x^5-2y)/x	\frac{dy}{dx}=\frac{x^{5}-2y}{x}
derivative of f(x)=e^{sqrt(x^3+1)}	derivative\:f(x)=e^{\sqrt{x^{3}+1}}
derivative of f(x)=\sqrt[3]{x^5}	derivative\:f(x)=\sqrt[3]{x^{5}}
derivative of y= 1/(sqrt(2x-1))	derivative\:y=\frac{1}{\sqrt{2x-1}}
derivative of f(x)=(x^3+5)/(x^2+1)	derivative\:f(x)=\frac{x^{3}+5}{x^{2}+1}
derivative of arccos(2x^2)	\frac{d}{dx}(\arccos(2x^{2}))
integral of sqrt(2+t^2)	\int\:\sqrt{2+t^{2}}dt
integral of 8/(x^2sqrt(x^2+25))	\int\:\frac{8}{x^{2}\sqrt{x^{2}+25}}dx
integral of 3/(sqrt(x)(1-cos(\sqrt{x)))}	\int\:\frac{3}{\sqrt{x}(1-\cos(\sqrt{x}))}dx
integral of sqrt((1-x^2))	\int\:\sqrt{(1-x^{2})}dx
derivative of t^{11}ln\|t\|	derivative\:t^{11}\ln\left\|t\right\|
integral of-1/pi cos(pix)	\int\:-\frac{1}{π}\cos(πx)dx
integral of (x^3-1)/(x^2+1)	\int\:\frac{x^{3}-1}{x^{2}+1}dx
derivative of cot^4(x)	\frac{d}{dx}(\cot^{4}(x))
derivative of (1-x/(1+x^2))	\frac{d}{dx}(\frac{1-x}{1+x^{2}})
derivative of e^{(xy})	\frac{d}{dx}(e^{(xy)})
integral of x+5	\int\:x+5dx
derivative of (-x^2)/2	derivative\:\frac{-x^{2}}{2}
derivative of-8e^{-4x^2}x	\frac{d}{dx}(-8e^{-4x^{2}}x)
integral of 1/(1+e^{-y)}	\int\:\frac{1}{1+e^{-y}}dy
derivative of f(x)=(x+x^{-1})^3	derivative\:f(x)=(x+x^{-1})^{3}
integral of tan^3(5x)	\int\:\tan^{3}(5x)dx
derivative of y=(ln\|x+8\|)^7	derivative\:y=(\ln\left\|x+8\right\|)^{7}
y^'=((3y^2-9))/(2xy)	y^{\prime\:}=\frac{(3y^{2}-9)}{2xy}
integral of (sin(x))^3(cos(x))^3	\int\:(\sin(x))^{3}(\cos(x))^{3}dx
derivative of e^{arcsin(x)}	derivative\:e^{\arcsin(x)}
(dy)/(dx)=-1/(2y)	\frac{dy}{dx}=-\frac{1}{2y}
integral from-1 to 1 of-2y^2+2	\int\:_{-1}^{1}-2y^{2}+2dy
y^{''}+18y^'+80y=0	y^{\prime\:\prime\:}+18y^{\prime\:}+80y=0
integral from 0 to 1 of (25)/(x^5)	\int\:_{0}^{1}\frac{25}{x^{5}}dx
integral from-3 to 0 of 9/(9x+4)	\int\:_{-3}^{0}\frac{9}{9x+4}dx
integral of (20)/(1+x^2)	\int\:\frac{20}{1+x^{2}}dx
sum from n=1 to infinity of 1/(ln(n))	\sum\:_{n=1}^{\infty\:}\frac{1}{\ln(n)}
(\partial)/(\partial y)(arctan(xy^2))	\frac{\partial\:}{\partial\:y}(\arctan(xy^{2}))
integral of 2te^{2t}	\int\:2te^{2t}dt
limit as x approaches 0-of 3/(e^x+1)	\lim\:_{x\to\:0-}(\frac{3}{e^{x}+1})
(\partial)/(\partial y)((x/y)e^{xy})	\frac{\partial\:}{\partial\:y}((\frac{x}{y})e^{xy})
(\partial)/(\partial z)(e^xsin(y))	\frac{\partial\:}{\partial\:z}(e^{x}\sin(y))
y^{''}-10y^'+25y=t^{-8}e^{5t}	y^{\prime\:\prime\:}-10y^{\prime\:}+25y=t^{-8}e^{5t}
integral of 7xe^{5x}	\int\:7xe^{5x}dx
integral of (2-3x)cos(4x)	\int\:(2-3x)\cos(4x)dx
(\partial)/(\partial x)(x^2+y^2)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2})
integral of sech(x)	\int\:\sech(x)dx
derivative of 4\sqrt[3]{x^7}-1/(x^2+2x)	\frac{d}{dx}(4\sqrt[3]{x^{7}}-\frac{1}{x^{2}}+2x)
tangent of 7x-7sqrt(x)	tangent\:7x-7\sqrt{x}
derivative of ((4x+1/(2-5x))^{1/3})	\frac{d}{dx}((\frac{4x+1}{2-5x})^{\frac{1}{3}})
derivative of f(x)=5x^2cos(x)-4x	derivative\:f(x)=5x^{2}\cos(x)-4x
derivative of y=arccos(2x+3)	derivative\:y=\arccos(2x+3)
inverse oflaplace 1/((s+1)(s-1)^2)	inverselaplace\:\frac{1}{(s+1)(s-1)^{2}}
xy^'-y=x^2+x-2	xy^{\prime\:}-y=x^{2}+x-2
derivative of y=6sqrt(8x^2+7)	derivative\:y=6\sqrt{8x^{2}+7}
slope of y=xsqrt(x)	slope\:y=x\sqrt{x}
(y-x+xycot(x))dx+xdy=0	(y-x+xy\cot(x))dx+xdy=0
integral of 1/x*e^{2x^2}	\int\:\frac{1}{x}\cdot\:e^{2x^{2}}dx
integral of x^3sqrt(9+x^2)	\int\:x^{3}\sqrt{9+x^{2}}dx
integral of 5sin(8x)cos(5x)	\int\:5\sin(8x)\cos(5x)dx
taylor 1/(5x+7)	taylor\:\frac{1}{5x+7}
(\partial)/(\partial x)(arcsin(11xyz))	\frac{\partial\:}{\partial\:x}(\arcsin(11xyz))
integral of (3x)/(\sqrt[3]{10-x^2)}	\int\:\frac{3x}{\sqrt[3]{10-x^{2}}}dx
derivative of (5x/(4x^2+1))	\frac{d}{dx}(\frac{5x}{4x^{2}+1})
derivative of e^xsin(x)+cos(x)e^x	derivative\:e^{x}\sin(x)+\cos(x)e^{x}
f(x)= 1/(4-x^2)	f(x)=\frac{1}{4-x^{2}}
integral from 1 to 4 of 3x-6	\int\:_{1}^{4}3x-6dx
integral from 1 to 2 of sqrt(x)(x-1)	\int\:_{1}^{2}\sqrt{x}(x-1)dx
(\partial)/(\partial y)(ye^x)	\frac{\partial\:}{\partial\:y}(ye^{x})
integral of 24x(6x^2-1)^5	\int\:24x(6x^{2}-1)^{5}dx
integral of (x+2)/(x^2+11x+18)	\int\:\frac{x+2}{x^{2}+11x+18}dx
integral from 0 to y of 8	\int\:_{0}^{y}8dx
tangent of f(x)=(3x-5)^{1/2},\at x=2	tangent\:f(x)=(3x-5)^{\frac{1}{2}},\at\:x=2
integral of 1/((25x^2+16)^2)	\int\:\frac{1}{(25x^{2}+16)^{2}}dx
derivative of-x^{-2}-1	\frac{d}{dx}(-x^{-2}-1)
derivative of (x^2+4*x+2)^9	derivative\:(x^{2}+4\cdot\:x+2)^{9}
derivative of f(x)= x/(x^2+196)	derivative\:f(x)=\frac{x}{x^{2}+196}
derivative of f(x)=x^2+x+1	derivative\:f(x)=x^{2}+x+1
limit as x approaches 1 of 3/(x^3-1)	\lim\:_{x\to\:1}(\frac{3}{x^{3}-1})
(\partial)/(\partial x)(2(x-a))	\frac{\partial\:}{\partial\:x}(2(x-a))
y^'+7y=4t	y^{\prime\:}+7y=4t
derivative of e^{4x^3}	\frac{d}{dx}(e^{4x^{3}})
limit as x approaches 0+of ln(x)	\lim\:_{x\to\:0+}(\ln(x))
integral from-2 to 1 of (x^4+x^3-4x^2+6)	\int\:_{-2}^{1}(x^{4}+x^{3}-4x^{2}+6)dx
y^5y^'=(x^5-3)e^{-y^6},y(0)=1	y^{5}y^{\prime\:}=(x^{5}-3)e^{-y^{6}},y(0)=1
integral of xsqrt(r^2-x^2)	\int\:x\sqrt{r^{2}-x^{2}}dx
derivative of 5cos(6ln(x))	\frac{d}{dx}(5\cos(6\ln(x)))
e^{7y}dy=cos(7x)dx	e^{7y}dy=\cos(7x)dx
integral from pi/4 to pi/2 of 1	\int\:_{\frac{π}{4}}^{\frac{π}{2}}1
integral of ((e^{1/x}))/(x^2)	\int\:\frac{(e^{\frac{1}{x}})}{x^{2}}dx
3(sin(t)y^'+cos(t)y)=cos(t)sin^2(t)	3(\sin(t)y^{\prime\:}+\cos(t)y)=\cos(t)\sin^{2}(t)
integral of arctan(9x)	\int\:\arctan(9x)dx
derivative of f(x)= 1/x+1/(x^2)	derivative\:f(x)=\frac{1}{x}+\frac{1}{x^{2}}
derivative of ((5x^5-3x^2+1))/x	derivative\:\frac{(5x^{5}-3x^{2}+1)}{x}
integral of 1/(12(x^2+1))	\int\:\frac{1}{12(x^{2}+1)}dx
limit as x approaches 3+of x/(x-3)	\lim\:_{x\to\:3+}(\frac{x}{x-3})
(1+x)y^'-xy=x+x^2	(1+x)y^{\prime\:}-xy=x+x^{2}

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