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Popular Calculus Problems

derivative of e^x(x-3)	\frac{d}{dx}(e^{x}(x-3))
area sqrt(x), 1/2 x,9	area\:\sqrt{x},\frac{1}{2}x,9
limit as x approaches-1+of 2x^3-2m	\lim\:_{x\to\:-1+}(2x^{3}-2m)
derivative of f(x)=5e^{2x}	derivative\:f(x)=5e^{2x}
(dy)/(dx)=(e^x)/(8+e^x)	\frac{dy}{dx}=\frac{e^{x}}{8+e^{x}}
derivative of e^{6x^2}	\frac{d}{dx}(e^{6x^{2}})
integral from 0 to 5 of 1/(x^{14/15)}	\int\:_{0}^{5}\frac{1}{x^{\frac{14}{15}}}dx
x^{''}-4x=0	x^{\prime\:\prime\:}-4x=0
integral of sin(t)*t	\int\:\sin(t)\cdot\:tdt
limit as x approaches 2 of x^2+8x-2	\lim\:_{x\to\:2}(x^{2}+8x-2)
integral from-1/2 to 1/2 of 1/(1-x^2)	\int\:_{-\frac{1}{2}}^{\frac{1}{2}}\frac{1}{1-x^{2}}dx
y^'=(x*y)/(1+x^2)	y^{\prime\:}=\frac{x\cdot\:y}{1+x^{2}}
integral of (x^3+x^2)^9(3x^2+2x)	\int\:(x^{3}+x^{2})^{9}(3x^{2}+2x)dx
integral of 7e^{4x}cos(8x)	\int\:7e^{4x}\cos(8x)dx
derivative of f(x)=2x-5	derivative\:f(x)=2x-5
integral of (108)/(w^2sqrt(36-w^2))	\int\:\frac{108}{w^{2}\sqrt{36-w^{2}}}dw
(dy)/(dx)=0.06y-24000	\frac{dy}{dx}=0.06y-24000
limit as x approaches infinity of 5.3	\lim\:_{x\to\:\infty\:}(5.3)
(\partial)/(\partial y)(yze^{xz})	\frac{\partial\:}{\partial\:y}(yze^{xz})
integral of sin((pit)/2)	\int\:\sin(\frac{πt}{2})dt
y^{''}-2/(t^2)y=0,y(-1)=-1,y^'(-1)=-4	y^{\prime\:\prime\:}-\frac{2}{t^{2}}y=0,y(-1)=-1,y^{\prime\:}(-1)=-4
integral of (2x^2+x+1)/((x+3)(x-1)^2)	\int\:\frac{2x^{2}+x+1}{(x+3)(x-1)^{2}}dx
sum from n=1 to infinity of 16^nx^nn!	\sum\:_{n=1}^{\infty\:}16^{n}x^{n}n!
integral of xsqrt(x^2+7)	\int\:x\sqrt{x^{2}+7}dx
integral of 1/(2000(2000-x))	\int\:\frac{1}{2000(2000-x)}dx
derivative of f(x)=x^a(1-x)^b	derivative\:f(x)=x^{a}(1-x)^{b}
tangent of f(x)=9-4x+6x^2,\at x=8	tangent\:f(x)=9-4x+6x^{2},\at\:x=8
(\partial)/(\partial y)(y^2e^{xy^2})	\frac{\partial\:}{\partial\:y}(y^{2}e^{xy^{2}})
integral of zsin(x)	\int\:z\sin(x)dy
tangent of 1/3 x^3+7/2 x^2-3x+5	tangent\:\frac{1}{3}x^{3}+\frac{7}{2}x^{2}-3x+5
f(t)=tan(t)	f(t)=\tan(t)
limit as x approaches 1 of e^{x^2-x}	\lim\:_{x\to\:1}(e^{x^{2}-x})
integral of sin^{12}(x)	\int\:\sin^{12}(x)dx
derivative of x-5sin(x)	\frac{d}{dx}(x-5\sin(x))
(d^2)/(dx^2)(sqrt(x+10))	\frac{d^{2}}{dx^{2}}(\sqrt{x+10})
derivative of x^{4/x}	\frac{d}{dx}(x^{\frac{4}{x}})
y^'=x(7-y)	y^{\prime\:}=x(7-y)
limit as x approaches 0 of 5(x-3)ln(x-3)	\lim\:_{x\to\:0}(5(x-3)\ln(x-3))
integral from-infinity to 0 of x/(1+x^2)	\int\:_{-\infty\:}^{0}\frac{x}{1+x^{2}}dx
derivative of (x^2/(x^2))	\frac{d}{dx}(\frac{x^{2}}{x^{2}})
derivative of (x^2+1\sqrt[3]{x^2+2})	\frac{d}{dx}((x^{2}+1)\sqrt[3]{x^{2}+2})
derivative of-3/x	derivative\:-\frac{3}{x}
integral of (x+4)/((x^2+8x-7)^2)	\int\:\frac{x+4}{(x^{2}+8x-7)^{2}}dx
d/(dt)(t+2)	\frac{d}{dt}(t+2)
integral of (3x-2)^5	\int\:(3x-2)^{5}dx
derivative of f(x)= 3/(\sqrt[4]{x)}	derivative\:f(x)=\frac{3}{\sqrt[4]{x}}
derivative of arcsin(sqrt(x))	derivative\:\arcsin(\sqrt{x})
(d^2)/(dx^2)(2xcos(x^2))	\frac{d^{2}}{dx^{2}}(2x\cos(x^{2}))
integral from 8 to 14 of y/(y^2-4y-5)	\int\:_{8}^{14}\frac{y}{y^{2}-4y-5}dy
y^'=e^{-2x}	y^{\prime\:}=e^{-2x}
tangent of f(x)=x^2+1	tangent\:f(x)=x^{2}+1
7y^{''}+5y^'+7y=0	7y^{\prime\:\prime\:}+5y^{\prime\:}+7y=0
limit as h approaches 0 of (4/(2+h)-2)/h	\lim\:_{h\to\:0}(\frac{\frac{4}{2+h}-2}{h})
area x=1-y^2,-x-1	area\:x=1-y^{2},-x-1
derivative of sqrt(2{p)(xx})	\frac{d}{dx}(\sqrt{2{p}(x)x})
derivative of arctan(x/3)	derivative\:\arctan(\frac{x}{3})
derivative of f(x)=x+sqrt(x)+2	derivative\:f(x)=x+\sqrt{x}+2
(\partial)/(\partial x)(xy(x-2)(y+3))	\frac{\partial\:}{\partial\:x}(xy(x-2)(y+3))
integral of xln(x+5)	\int\:x\ln(x+5)dx
(\partial)/(\partial x)(ln(x^2+y^5))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{5}))
integral of ln(sqrt(x+2))	\int\:\ln(\sqrt{x+2})dx
integral of 7x^3e^x	\int\:7x^{3}e^{x}dx
tangent of f(x)=x^2-3x+4,\at x=1	tangent\:f(x)=x^{2}-3x+4,\at\:x=1
(dy)/(dt)+2ty=2te^{-t^2}	\frac{dy}{dt}+2ty=2te^{-t^{2}}
(\partial)/(\partial z)(xycos(z))	\frac{\partial\:}{\partial\:z}(xy\cos(z))
integral of x^6-4x^4+x+1	\int\:x^{6}-4x^{4}+x+1dx
integral of (t^5)/(sqrt(t^2+10))	\int\:\frac{t^{5}}{\sqrt{t^{2}+10}}dt
(dy)/(dx)=0.5(100-y)	\frac{dy}{dx}=0.5(100-y)
integral from 1 to 5 of sqrt(x)ln(x)	\int\:_{1}^{5}\sqrt{x}\ln(x)dx
derivative of f(x)=x(x+3)^2	derivative\:f(x)=x(x+3)^{2}
y^'-2y=7	y^{\prime\:}-2y=7
(\partial)/(\partial x)(x+yz)	\frac{\partial\:}{\partial\:x}(x+yz)
derivative of 6+x	\frac{d}{dx}(6+x)
limit as x approaches 0 of (8/(1+x)-8)/x	\lim\:_{x\to\:0}(\frac{\frac{8}{1+x}-8}{x})
integral of (1-(x+2)cot(x))/(sin(x))	\int\:\frac{1-(x+2)\cot(x)}{\sin(x)}dx
derivative of log_{6}(x^2-5x)	derivative\:\log_{6}(x^{2}-5x)
integral from 0 to pi/3 of 7sec^2(x)	\int\:_{0}^{\frac{π}{3}}7\sec^{2}(x)dx
(\partial)/(\partial x)(3ln(x))	\frac{\partial\:}{\partial\:x}(3\ln(x))
area (sqrt(x+6)),x,-2,3	area\:(\sqrt{x+6}),x,-2,3
integral of sec^6(x)tan(x)	\int\:\sec^{6}(x)\tan(x)dx
derivative of y=sqrt(ln(7x))	derivative\:y=\sqrt{\ln(7x)}
derivative of e^{x^3+3x}	\frac{d}{dx}(e^{x^{3}+3x})
limit as x approaches 2 of (\|x-2\|)/2	\lim\:_{x\to\:2}(\frac{\left\|x-2\right\|}{2})
slope of 10(1.05)^x	slope\:10(1.05)^{x}
integral from 0 to pi of cos(t)sin(t)	\int\:_{0}^{π}\cos(t)\sin(t)dt
sum from n=0 to infinity of (x^n)/n	\sum\:_{n=0}^{\infty\:}\frac{x^{n}}{n}
derivative of 3,x	\frac{d}{dx}(3,x)
limit as x approaches+0 of (sqrt(x))/x	\lim\:_{x\to\:+0}(\frac{\sqrt{x}}{x})
derivative of (x^3-3xln(2x+1))	\frac{d}{dx}((x^{3}-3x)\ln(2x+1))
y^{''}-2y^'+10y=x^2*e^x	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=x^{2}\cdot\:e^{x}
tangent of f(x)=(5x-x^2)(5-x-x^2),\at x=1	tangent\:f(x)=(5x-x^{2})(5-x-x^{2}),\at\:x=1
tangent of f(x)=sqrt(x-3)	tangent\:f(x)=\sqrt{x-3}
laplacetransform 1/2 cos(2t)	laplacetransform\:\frac{1}{2}\cos(2t)
integral of 1/(usqrt(a^2-u^2))	\int\:\frac{1}{u\sqrt{a^{2}-u^{2}}}du
(\partial)/(\partial z)(cos(xyz))	\frac{\partial\:}{\partial\:z}(\cos(xyz))
(dy)/(dt)=1.4y	\frac{dy}{dt}=1.4y
integral of 1/(-x^2-1)	\int\:\frac{1}{-x^{2}-1}dx
derivative of y=\sqrt[3]{t}(t^2+4)	derivative\:y=\sqrt[3]{t}(t^{2}+4)
y^'=((xy^3))/(25)	y^{\prime\:}=\frac{(xy^{3})}{25}
integral of-18t+4	\int\:-18t+4dt

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