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Popular Calculus Problems

(\partial)/(\partial x)(1/((x+y)))	\frac{\partial\:}{\partial\:x}(\frac{1}{(x+y)})
integral of 4t^4e^{6t^5}	\int\:4t^{4}e^{6t^{5}}dt
limit as n approaches infinity of (1)^n	\lim\:_{n\to\:\infty\:}((1)^{n})
(dy)/(dx)(x+y)=x-y	\frac{dy}{dx}(x+y)=x-y
d/(dt)(-e^{2t})	\frac{d}{dt}(-e^{2t})
limit as x approaches 0 of (cos(2x)-cos(5x))/(x^2)	\lim\:_{x\to\:0}(\frac{\cos(2x)-\cos(5x)}{x^{2}})
integral of e^{5x}cos(3x)	\int\:e^{5x}\cos(3x)dx
integral of cos(2x)-sin(x/2)	\int\:\cos(2x)-\sin(\frac{x}{2})dx
laplacetransform tsin(kt)	laplacetransform\:t\cdot\:\sin(k\cdot\:t)
limit as x approaches-4 of sqrt(-5x-8)	\lim\:_{x\to\:-4}(\sqrt{-5x-8})
xy^'-2y=x^2-x-2	xy^{\prime\:}-2y=x^{2}-x-2
y^'=xe^{y-x^2}	y^{\prime\:}=xe^{y-x^{2}}
area x=2y^2,x=2	area\:x=2y^{2},x=2
y^{''}-2y^'-15y=e^{(3x)}cos(2x)	y^{\prime\:\prime\:}-2y^{\prime\:}-15y=e^{(3x)}\cos(2x)
integral of ((1-sqrt(z)))/(zsqrt(z))	\int\:\frac{(1-\sqrt{z})}{z\sqrt{z}}dz
derivative of cos(pix)	derivative\:\cos(πx)
limit as x approaches 8 of 88	\lim\:_{x\to\:8}(88)
derivative of f(x)=2^{x^3}	derivative\:f(x)=2^{x^{3}}
y=x^x+1	y=x^{x}+1
slope of (-2,-1),(4,2)	slope\:(-2,-1),(4,2)
derivative of 3+2x	\frac{d}{dx}(3+2x)
tangent of f(x)= x/(x-2),\at x=1	tangent\:f(x)=\frac{x}{x-2},\at\:x=1
limit as x approaches 1 of arcsec(x)	\lim\:_{x\to\:1}(\arcsec(x))
derivative of sqrt(x^3)+1/(sqrt(x))	\frac{d}{dx}(\sqrt{x^{3}}+\frac{1}{\sqrt{x}})
derivative of 7e^xcos(x)	derivative\:7e^{x}\cos(x)
integral of 1/(5x^5)	\int\:\frac{1}{5x^{5}}dx
integral from 0 to 8 of sqrt(64-x^2)	\int\:_{0}^{8}\sqrt{64-x^{2}}dx
(x^2+1)((dy)/(dx))+8x(y-1)=0,y(0)=5	(x^{2}+1)(\frac{dy}{dx})+8x(y-1)=0,y(0)=5
6x+(dy)/(dx)=0	6x+\frac{dy}{dx}=0
derivative of 1/({f(x)})	\frac{d}{dx}(\frac{1}{{f}(x)})
integral from 1 to-1 of (x-1)(3x+2)	\int\:_{1}^{-1}(x-1)(3x+2)dx
integral from 10 to 13 of 2x	\int\:_{10}^{13}2xdx
derivative of y=4x-3x^2	derivative\:y=4x-3x^{2}
limit as x approaches infinity of (4^x)/(3^{x-1)}	\lim\:_{x\to\:\infty\:}(\frac{4^{x}}{3^{x-1}})
(\partial)/(\partial x)(y/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{y^{2}+x^{2}})
integral from 2 to 8 of (10-x)	\int\:_{2}^{8}(10-x)dx
derivative of ,xe^y+y^2x-x^3,\at (1,0)	\frac{d}{dx}(,xe^{y}+y^{2}x-x^{3},\at\:(1,0))
integral of x^2arcsin(x)	\int\:x^{2}\arcsin(x)dx
derivative of-2/(5sqrt(x))	\frac{d}{dx}(-\frac{2}{5\sqrt{x}})
derivative of (x+2/(ln(x)))	\frac{d}{dx}(\frac{x+2}{\ln(x)})
(\partial}{\partial y}(e^{y/x}-\frac{e^{y/x}y)/x)	\frac{\partial\:}{\partial\:y}(e^{\frac{y}{x}}-\frac{e^{\frac{y}{x}}y}{x})
integral from 0 to 1 of xsqrt(1-x)	\int\:_{0}^{1}x\sqrt{1-x}dx
solvefor x,(d^2x)/(dt^2)+x=(t^2+t)sin(t)	solvefor\:x,\frac{d^{2}x}{dt^{2}}+x=(t^{2}+t)\sin(t)
slope of (-5,11),(-10,6)	slope\:(-5,11),(-10,6)
integral of (ln(2x))/(x^2)	\int\:\frac{\ln(2x)}{x^{2}}dx
y^{1/2}((dy)/(dx))+y^{3/2}=1,y(0)=9	y^{\frac{1}{2}}(\frac{dy}{dx})+y^{\frac{3}{2}}=1,y(0)=9
sum from n=1 to infinity}\sqrt{5 of*2/n	\sum\:_{n=1}^{\infty\:}\sqrt{5}\cdot\:\frac{2}{n}
limit as x approaches 6 of (x^2-9x+18)/(x-6)	\lim\:_{x\to\:6}(\frac{x^{2}-9x+18}{x-6})
area y=6x,y= 3/2 x,y=7-x^2	area\:y=6x,y=\frac{3}{2}x,y=7-x^{2}
integral of e^{2x^2}x	\int\:e^{2x^{2}}xdx
integral of (kx)/(sqrt(1-x))	\int\:\frac{kx}{\sqrt{1-x}}dx
integral from 0 to pi/2 of sec^4(t/2)	\int\:_{0}^{\frac{π}{2}}\sec^{4}(\frac{t}{2})dt
integral of ((5x^3-3\sqrt[5]{x})/(5x))	\int\:(\frac{5x^{3}-3\sqrt[5]{x}}{5x})dx
derivative of f(x)=((x+7)/(x+9))^6	derivative\:f(x)=(\frac{x+7}{x+9})^{6}
integral of y^2e^{3y}	\int\:y^{2}e^{3y}dy
derivative of-2cos(x-x)	\frac{d}{dx}(-2\cos(x)-x)
integral of 1/(t^2)cos(1/t-1)	\int\:\frac{1}{t^{2}}\cos(\frac{1}{t}-1)dt
derivative of ln(arctan(x+1))	derivative\:\ln(\arctan(x+1))
(dy)/(dx)=(cos(8x))/(e^{8y)}	\frac{dy}{dx}=\frac{\cos(8x)}{e^{8y}}
derivative of g(x)=(5-x)^2(2x-1)^5	derivative\:g(x)=(5-x)^{2}(2x-1)^{5}
integral from-8 to 10 of x/2+10	\int\:_{-8}^{10}\frac{x}{2}+10dx
tangent of g(x)=x^2-8,\at x=-3	tangent\:g(x)=x^{2}-8,\at\:x=-3
x^2y^{''}+xy^'+4y=0	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}+4y=0
tangent of f(x)=x^2-5x+5,(0,5)	tangent\:f(x)=x^{2}-5x+5,(0,5)
d/(dt)(e^t(cos(t)))	\frac{d}{dt}(e^{t}(\cos(t)))
integral from 0 to 3/4 of 1/(9+16x^2)	\int\:_{0}^{\frac{3}{4}}\frac{1}{9+16x^{2}}dx
derivative of 1/(sqrt(2pi)e^{-(x^2)/2})	\frac{d}{dx}(\frac{1}{\sqrt{2π}}e^{-\frac{x^{2}}{2}})
derivative of Ax^2e^x+Bxe^x+Ce^x	\frac{d}{dx}(Ax^{2}e^{x}+Bxe^{x}+Ce^{x})
integral of 1/(10x)	\int\:\frac{1}{10x}dx
derivative of y^2	derivative\:y^{2}
f^'(x)=3arctan(x^2-3x+2)	f^{\prime\:}(x)=3\arctan(x^{2}-3x+2)
integral of (sin(2x))/(cos^3(2x))	\int\:\frac{\sin(2x)}{\cos^{3}(2x)}dx
derivative of f(z)=(9z^4+3z^2+1)(3z^3-z)	derivative\:f(z)=(9z^{4}+3z^{2}+1)(3z^{3}-z)
integral of (4-2x)^2	\int\:(4-2x)^{2}dx
limit as x approaches-8 of 9x+10	\lim\:_{x\to\:-8}(9x+10)
((dx))/((dy))=(8-(2x))/((100+2y))	\frac{(dx)}{(dy)}=\frac{8-(2x)}{(100+2y)}
derivative of f(x)=e^{xsqrt(7x+6)}	derivative\:f(x)=e^{x\sqrt{7x+6}}
inverse oflaplace 7/(2s^{2+8)}	inverselaplace\:\frac{7}{2s^{2+8}}
integral of cos^{2-2}(x)	\int\:\cos^{2-2}(x)dx
derivative of (x^6/(12)+1/(8x^4))	\frac{d}{dx}(\frac{x^{6}}{12}+\frac{1}{8x^{4}})
slope of (3,-9),(52,1)	slope\:(3,-9),(52,1)
integral from 6 to 9 of y/(y^2-2y-3)	\int\:_{6}^{9}\frac{y}{y^{2}-2y-3}dy
(\partial)/(\partial x)(3xyln(xy))	\frac{\partial\:}{\partial\:x}(3xy\ln(xy))
tangent of x^4-y^2=7,(2,3)	tangent\:x^{4}-y^{2}=7,(2,3)
integral of cos^7(9-x)sin(9-x)	\int\:\cos^{7}(9-x)\sin(9-x)dx
v'-2=2v^2	v\prime\:-2=2v^{2}
derivative of (2x+7^3)	\frac{d}{dx}((2x+7)^{3})
(\partial)/(\partial x)(3x^2(5x+7y))	\frac{\partial\:}{\partial\:x}(3x^{2}(5x+7y))
tan(x)(dy)/(dx)=y	\tan(x)\frac{dy}{dx}=y
limit as x approaches 5 of (x^2-3x-10)/(x^2-10x+25)	\lim\:_{x\to\:5}(\frac{x^{2}-3x-10}{x^{2}-10x+25})
derivative of 6x^2	derivative\:6x^{2}
derivative of (sqrt(x)+1/(\sqrt[3]{x})^2)	\frac{d}{dx}((\sqrt{x}+\frac{1}{\sqrt[3]{x}})^{2})
y^'=(t^2)/y	y^{\prime\:}=\frac{t^{2}}{y}
integral of (x^3)/(sqrt(x^2+49))	\int\:\frac{x^{3}}{\sqrt{x^{2}+49}}dx
integral of (1/2 x)	\int\:(\frac{1}{2}x)dx
taylor e^{-h}+e^h	taylor\:e^{-h}+e^{h}
derivative of 20(1+e^{10-t})^{-1}	derivative\:20(1+e^{10-t})^{-1}
y^'=8xy	y^{\prime\:}=8xy
(\partial)/(\partial x)(x^4+y^2-4)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{2}-4)
y^{''}-y^'-2y=e^{2t}	y^{\prime\:\prime\:}-y^{\prime\:}-2y=e^{2t}

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