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Popular Calculus Problems

limit as x approaches infinity of (1-5x)^{5/x}	\lim\:_{x\to\:\infty\:}((1-5x)^{\frac{5}{x}})
limit as x approaches 1/2 of 2x+7	\lim\:_{x\to\:\frac{1}{2}}(2x+7)
derivative of cos(2x-xln(x))	\frac{d}{dx}(\cos(2x)-x\ln(x))
integral from 0 to 1 of (8x^e+5e^x)	\int\:_{0}^{1}(8x^{e}+5e^{x})dx
(d^2)/(dx^2)((30x)/((x^2+6)^2))	\frac{d^{2}}{dx^{2}}(\frac{30x}{(x^{2}+6)^{2}})
derivative of 7y	derivative\:7y
integral of 1/(16x^4+8x^2+1)	\int\:\frac{1}{16x^{4}+8x^{2}+1}dx
(\partial)/(\partial x)(sin(kx))	\frac{\partial\:}{\partial\:x}(\sin(kx))
integral of 3x\sqrt[3]{2-x^2}	\int\:3x\sqrt[3]{2-x^{2}}dx
integral of (x+2)sqrt(x+1)	\int\:(x+2)\sqrt{x+1}dx
y^{''}=y+4t^2	y^{\prime\:\prime\:}=y+4t^{2}
limit as x approaches 5 of-3x	\lim\:_{x\to\:5}(-3x)
tangent of y=7e^{-6x},(0,7)	tangent\:y=7e^{-6x},(0,7)
(dy)/(dx)=9x-y/x	\frac{dy}{dx}=9x-\frac{y}{x}
y^{''}-2y^'=4t,y(0)=2,y^'(0)=0	y^{\prime\:\prime\:}-2y^{\prime\:}=4t,y(0)=2,y^{\prime\:}(0)=0
(\partial)/(\partial x)(-sqrt(x^2+y^2-1))	\frac{\partial\:}{\partial\:x}(-\sqrt{x^{2}+y^{2}-1})
derivative of (6x-x^2^{1/2})	\frac{d}{dx}((6x-x^{2})^{\frac{1}{2}})
integral of tcos(t)sin(t)	\int\:t\cos(t)\sin(t)dt
derivative of 2/(7x^3)	\frac{d}{dx}(\frac{2}{7x^{3}})
derivative of 1/(sqrt(a^2-x^2))	\frac{d}{dx}(\frac{1}{\sqrt{a^{2}-x^{2}}})
limit as x approaches 6 of 5x+\|x-6\|	\lim\:_{x\to\:6}(5x+\left\|x-6\right\|)
(\partial)/(\partial x)(20arccot(x))	\frac{\partial\:}{\partial\:x}(20\arccot(x))
integral from 6 to 12 of (6e^x)	\int\:_{6}^{12}(6e^{x})dx
integral of sqrt((9-x)/(9+x))	\int\:\sqrt{\frac{9-x}{9+x}}dx
derivative of mxn+b+b^8x^3m-5+nx^2b-2	\frac{d}{dx}(mxn+b+b^{8}x^{3}m-5+nx^{2}b-2)
derivative of f(x)=(e^2)/(x^2-2x)	derivative\:f(x)=\frac{e^{2}}{x^{2}-2x}
integral of (7/(sqrt(x)))	\int\:(\frac{7}{\sqrt{x}})dx
limit as p approaches 0 of p^2sin(1/p)	\lim\:_{p\to\:0}(p^{2}\sin(\frac{1}{p}))
y^{''}-18y^'+117y=0	y^{\prime\:\prime\:}-18y^{\prime\:}+117y=0
limit as x approaches 1/2 of (x+4)/(2x)	\lim\:_{x\to\:\frac{1}{2}}(\frac{x+4}{2x})
derivative of 3/(sqrt(x+2))	\frac{d}{dx}(\frac{3}{\sqrt{x+2}})
integral of 4/(y^2+5y-14)	\int\:\frac{4}{y^{2}+5y-14}dy
integral from 0 to 21 of-x(x-21)(x+1)	\int\:_{0}^{21}-x(x-21)(x+1)dx
derivative of (x^x)	\frac{d}{dx}((x)^{x})
y^'+y/(10)=500	y^{\prime\:}+\frac{y}{10}=500
(dN)/(dt)=N(1-0.0002N)	\frac{dN}{dt}=N(1-0.0002N)
derivative of c_{1}cos(2x+c_{2}sin(2x))	\frac{d}{dx}(c_{1}\cos(2x)+c_{2}\sin(2x))
derivative of sec(1/2 xtan(1/2 x))	\frac{d}{dx}(\sec(\frac{1}{2}x)\tan(\frac{1}{2}x))
derivative of a/(x^2+b)	\frac{d}{dx}(\frac{a}{x^{2}+b})
derivative of y=x^8	derivative\:y=x^{8}
d/(dy)(x^2+2xy+y^2)	\frac{d}{dy}(x^{2}+2xy+y^{2})
integral of xcos((npix)/l)	\int\:x\cos(\frac{nπx}{l})dx
integral of (4x+2)ln(x+1)	\int\:(4x+2)\ln(x+1)dx
limit as x approaches 1 of 1-x^2	\lim\:_{x\to\:1}(1-x^{2})
taylor 2^x,0	taylor\:2^{x},0
integral of 1/(sqrt(625+x^2))	\int\:\frac{1}{\sqrt{625+x^{2}}}dx
integral of x^4*e^{12x}	\int\:x^{4}\cdot\:e^{12x}dx
2xy^'+y=2sqrt(x)	2xy^{\prime\:}+y=2\sqrt{x}
(\partial)/(\partial x)(xe^{sqrt(xy)})	\frac{\partial\:}{\partial\:x}(xe^{\sqrt{xy}})
tangent of y=x^2+5x+3,\at x=1	tangent\:y=x^{2}+5x+3,\at\:x=1
derivative of 3(5-7x^5)	\frac{d}{dx}(3(5-7x)^{5})
(\partial)/(\partial x)(x^{3/4}y^{-4})	\frac{\partial\:}{\partial\:x}(x^{\frac{3}{4}}y^{-4})
integral of xsin^2(x)	\int\:x\sin^{2}(x)dx
integral of (x^2-1)e^{2x}	\int\:(x^{2}-1)e^{2x}dx
y^{''}-6y^'+4y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+4y=0
integral from 0 to x of e^{t^2}	\int\:_{0}^{x}e^{t^{2}}dt
integral of (4+3x)e^{-x}	\int\:(4+3x)e^{-x}dx
(\partial)/(\partial x)(2xe^x)	\frac{\partial\:}{\partial\:x}(2xe^{x})
derivative of f(x)=sqrt(6)x+sqrt(7x)	derivative\:f(x)=\sqrt{6}x+\sqrt{7x}
limit as x approaches 3 of (-2x)/(x-3)	\lim\:_{x\to\:3}(\frac{-2x}{x-3})
integral of 6/(sqrt(8-3x))	\int\:\frac{6}{\sqrt{8-3x}}dx
tangent of f(x)= 4/x ,\at x=-9	tangent\:f(x)=\frac{4}{x},\at\:x=-9
limit as x approaches infinity of ln(x!)	\lim\:_{x\to\:\infty\:}(\ln(x!))
integral of (2x^2+1)/(x(x-1)^3)	\int\:\frac{2x^{2}+1}{x(x-1)^{3}}dx
derivative of (3x^2-6x+6e^x)	\frac{d}{dx}((3x^{2}-6x+6)e^{x})
sum from n=1 to infinity of 3/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{3}{4^{n}}
integral of 3x^2sqrt(1+x^3)	\int\:3x^{2}\sqrt{1+x^{3}}dx
integral from 0 to h of 1/(2sqrt(hx))	\int\:_{0}^{h}\frac{1}{2\sqrt{hx}}dx
integral of (x^2+5)ln(x)	\int\:(x^{2}+5)\ln(x)dx
derivative of 7x^6-9cos(x)	derivative\:7x^{6}-9\cos(x)
derivative of (\sqrt[3]{x})/x	derivative\:\frac{\sqrt[3]{x}}{x}
derivative of (4x^2+3(4x-5))	\frac{d}{dx}((4x^{2}+3)(4x-5))
integral from 3.5 to 5 of x/8	\int\:_{3.5}^{5}\frac{x}{8}dx
integral of (-16)/(sqrt(4-x^2))	\int\:\frac{-16}{\sqrt{4-x^{2}}}dx
integral of x(1-x^2)^2	\int\:x(1-x^{2})^{2}dx
y^{''}+2y^'+2y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=0,y(0)=1,y^{\prime\:}(0)=0
derivative of-2(x^2+3x)	derivative\:-2(x^{2}+3x)
laplacetransform 2t^2-2t+1	laplacetransform\:2t^{2}-2t+1
(dy}{dt}=\frac{2y)/t	\frac{dy}{dt}=\frac{2y}{t}
x^2y^2(dy)/(dx)=1	x^{2}y^{2}\frac{dy}{dx}=1
derivative of f(x)=e^{-x+1}x-2e^{-x+1}	derivative\:f(x)=e^{-x+1}x-2e^{-x+1}
implicit 4xy=sin(x+y)	implicit\:4xy=\sin(x+y)
tangent of y=x^2-2x-4,(2,-4)	tangent\:y=x^{2}-2x-4,(2,-4)
derivative of sqrt(1+sin(2x))	\frac{d}{dx}(\sqrt{1+\sin(2x)})
integral of (2x^4-2x^2)/(x^2)	\int\:\frac{2x^{4}-2x^{2}}{x^{2}}dx
derivative of sqrt(r)+\sqrt[6]{r}	derivative\:\sqrt{r}+\sqrt[6]{r}
derivative of ln(x+sqrt(1+x^2))	derivative\:\ln(x+\sqrt{1+x^{2}})
(\partial)/(\partial y)(x^3+xy)	\frac{\partial\:}{\partial\:y}(x^{3}+xy)
limit as x approaches infinity of (256^{x/2})/(4^{2x)}	\lim\:_{x\to\:\infty\:}(\frac{256^{\frac{x}{2}}}{4^{2x}})
integral of 6/(x^2+4)	\int\:\frac{6}{x^{2}+4}dx
limit as x approaches 1 of (x^2+1)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{2}+1}{x-1})
limit as x approaches 3 of 2ln(x-4)	\lim\:_{x\to\:3}(2\ln(x-4))
integral of 12(y-1)x^3e^{2x(y-1)}	\int\:12(y-1)x^{3}e^{2x(y-1)}dy
integral of 4/((x^2+1)^2)	\int\:\frac{4}{(x^{2}+1)^{2}}dx
derivative of f(x)=(x^2-3)(x^2-sqrt(2))	derivative\:f(x)=(x^{2}-3)(x^{2}-\sqrt{2})
derivative of ln(\sqrt[3]{x^2})	\frac{d}{dx}(\ln(\sqrt[3]{x^{2}}))
derivative of g(t)= 3/(4t^6)	derivative\:g(t)=\frac{3}{4t^{6}}
integral of (2x+3)^5	\int\:(2x+3)^{5}dx
derivative of 7/(sqrt(x+9))	\frac{d}{dx}(\frac{7}{\sqrt{x+9}})
(\partial)/(\partial x)(e^{-x}cos(piy))	\frac{\partial\:}{\partial\:x}(e^{-x}\cos(πy))

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