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Popular Calculus Problems

tangent of f(x)=csc(x),\at x= pi/6	tangent\:f(x)=\csc(x),\at\:x=\frac{π}{6}
derivative of y^3+xy^2+y	\frac{d}{dx}(y^{3}+xy^{2}+y)
derivative of ((x+1)(x^2+1))/(x-2)	derivative\:\frac{(x+1)(x^{2}+1)}{x-2}
integral from-1 to 1 of (6x^5+3)	\int\:_{-1}^{1}(6x^{5}+3)dx
derivative of y=(9x)/(e^x)	derivative\:y=\frac{9x}{e^{x}}
f(x)=(x+1)/(x^2+1)	f(x)=\frac{x+1}{x^{2}+1}
(dy)/(dx)-3y=2	\frac{dy}{dx}-3y=2
integral of 1/((x^2-9))	\int\:\frac{1}{(x^{2}-9)}dx
integral of 3(3x+4)5	\int\:3(3x+4)5dx
(dy)/(dx)y=(2x+8)^3	\frac{dy}{dx}y=(2x+8)^{3}
integral of e^{4x}sin(2x)	\int\:e^{4x}\sin(2x)dx
(\partial)/(\partial x)(4x^3y^2-4)	\frac{\partial\:}{\partial\:x}(4x^{3}y^{2}-4)
integral of 12x^{5/7}+7x^{-6/7}	\int\:12x^{\frac{5}{7}}+7x^{-\frac{6}{7}}dx
y^'=((3x^2+y^2))/(xy)	y^{\prime\:}=\frac{(3x^{2}+y^{2})}{xy}
integral of cox	\int\:coxdx
integral from 1 to 16 of x/(sqrt(x))	\int\:_{1}^{16}\frac{x}{\sqrt{x}}dx
y^'=(x-3)e^{-2y}	y^{\prime\:}=(x-3)e^{-2y}
derivative of-4/((5)^3)	derivative\:-\frac{4}{(5)^{3}}
limit as x approaches-1 of x^2-x+7	\lim\:_{x\to\:-1}(x^{2}-x+7)
derivative of f(x)=ln(3+sqrt(x))	derivative\:f(x)=\ln(3+\sqrt{x})
(dy)/(dx)=(y^2+6xsqrt(x^2+y^2))/(xy)	\frac{dy}{dx}=\frac{y^{2}+6x\sqrt{x^{2}+y^{2}}}{xy}
tangent of f(x)=2(x^2-1)^3,\at x=2	tangent\:f(x)=2(x^{2}-1)^{3},\at\:x=2
limit as x approaches-8+of (2x)/(x+8)	\lim\:_{x\to\:-8+}(\frac{2x}{x+8})
derivative of f(x)= 2/(sqrt(4x+3))	derivative\:f(x)=\frac{2}{\sqrt{4x+3}}
derivative of f(x)=(1-3x)/(1+3x)	derivative\:f(x)=\frac{1-3x}{1+3x}
limit as x approaches 3/4 of (4x^2-9)/(2x-3)	\lim\:_{x\to\:\frac{3}{4}}(\frac{4x^{2}-9}{2x-3})
integral from 0 to 3 of 3-x	\int\:_{0}^{3}3-xdx
(4sin(x))^'	(4\sin(x))^{\prime\:}
integral of 1/(49e^{-9x)+e^{9x}}	\int\:\frac{1}{49e^{-9x}+e^{9x}}dx
integral of (x^2)/(2sqrt(x))	\int\:\frac{x^{2}}{2\sqrt{x}}dx
integral of (x^3+6x)^5(6x^2+12)	\int\:(x^{3}+6x)^{5}(6x^{2}+12)dx
derivative of (ax-b/(x^2-1))	\frac{d}{dx}(\frac{ax-b}{x^{2}-1})
integral from 0 to 4 of (4-t)sqrt(t)	\int\:_{0}^{4}(4-t)\sqrt{t}dt
tangent of f(x)=x-4/x ,\at 0	tangent\:f(x)=x-\frac{4}{x},\at\:0
2y^{''}+4y^'=0	2y^{\prime\:\prime\:}+4y^{\prime\:}=0
y^'+2y=2	y^{\prime\:}+2y=2
derivative of 5x^3log_{3}(x)	derivative\:5x^{3}\log_{3}(x)
integral of 0.8sin(x)+(1.6)/(pi^2)x	\int\:0.8\sin(x)+\frac{1.6}{π^{2}}xdx
(\partial)/(\partial z)(tan(5+2x^2y^4z^2))	\frac{\partial\:}{\partial\:z}(\tan(5+2x^{2}y^{4}z^{2}))
(dy)/(dx)=5^{tan(5x)}	\frac{dy}{dx}=5^{\tan(5x)}
y^{''}-2/(t^2)y=0	y^{\prime\:\prime\:}-\frac{2}{t^{2}}y=0
(\partial)/(\partial x)(x^3sin(x^2))	\frac{\partial\:}{\partial\:x}(x^{3}\sin(x^{2}))
integral from 1 to 2 of 9/(x^3+2x)	\int\:_{1}^{2}\frac{9}{x^{3}+2x}dx
y^{''}+5y^'+6y=0	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=0
y^{''}+3y=9	y^{\prime\:\prime\:}+3y=9
derivative of (x^2+3/(x^2-3x))	\frac{d}{dx}(\frac{x^{2}+3}{x^{2}-3x})
integral of sqrt(4r^2+1)r	\int\:\sqrt{4r^{2}+1}rdr
derivative of arccos(x/8)	\frac{d}{dx}(\arccos(\frac{x}{8}))
derivative of pi^x	\frac{d}{dx}(π^{x})
integral of 1/(xsqrt(9x^2-25))	\int\:\frac{1}{x\sqrt{9x^{2}-25}}dx
(dy)/(dx)= 4/(x^2e^{2y)}	\frac{dy}{dx}=\frac{4}{x^{2}e^{2y}}
integral of sin(sqrt(x))	\int\:\sin(\sqrt{x})dx
(\partial)/(\partial x)(6x^7y^4+2x^6y^8)	\frac{\partial\:}{\partial\:x}(6x^{7}y^{4}+2x^{6}y^{8})
slope of 4y^3+7x^8=5y+6x,(1,1)	slope\:4y^{3}+7x^{8}=5y+6x,(1,1)
sum from n=1 to infinity of (5/2)^n	\sum\:_{n=1}^{\infty\:}(\frac{5}{2})^{n}
derivative of (((x^3+8)/(2x))^7)	\frac{d}{dx}((\frac{(x^{3}+8)}{2x})^{7})
derivative of u^6	derivative\:u^{6}
limit as x approaches 0 of (1/x)^x	\lim\:_{x\to\:0}((\frac{1}{x})^{x})
integral of 1/((3x+2)^2)	\int\:\frac{1}{(3x+2)^{2}}dx
sum from n=2 to infinity of (n+4)/(n!)	\sum\:_{n=2}^{\infty\:}\frac{n+4}{n!}
longdivision (x^2-1)/(x^2+1)	longdivision\:\frac{x^{2}-1}{x^{2}+1}
area 2y=5,y=3,2y+3x=8	area\:2y=5,y=3,2y+3x=8
taylor (x^2)/(1-x^2)	taylor\:\frac{x^{2}}{1-x^{2}}
(\partial)/(\partial x)(xy^2arctan(z))	\frac{\partial\:}{\partial\:x}(xy^{2}\arctan(z))
y^{''}-2y-3y=3e^{2x}	y^{\prime\:\prime\:}-2y-3y=3e^{2x}
derivative of y=sqrt(x)^{7x}	derivative\:y=\sqrt{x}^{7x}
laplacetransform t^3e^{-3t}	laplacetransform\:t^{3}e^{-3t}
limit as x approaches 0 of 6^x	\lim\:_{x\to\:0}(6^{x})
(\partial)/(\partial x)(x^3y^7)	\frac{\partial\:}{\partial\:x}(x^{3}y^{7})
laplacetransform-5t^2e^{-4t}+sin(3t)	laplacetransform\:-5t^{2}e^{-4t}+\sin(3t)
derivative of x^3-7x^2+14x-6	\frac{d}{dx}(x^{3}-7x^{2}+14x-6)
(\partial)/(\partial u)(u/(v+1))	\frac{\partial\:}{\partial\:u}(\frac{u}{v+1})
integral of ge^{-2ct}	\int\:ge^{-2ct}dt
limit as x approaches-1 of (x+1)/(1-x^2)	\lim\:_{x\to\:-1}(\frac{x+1}{1-x^{2}})
limit as x approaches 5+of 5/(x-5)	\lim\:_{x\to\:5+}(\frac{5}{x-5})
integral of cos(2x)sin(3x)	\int\:\cos(2x)\sin(3x)dx
taylor x^{1/3},8	taylor\:x^{\frac{1}{3}},8
derivative of 1/(x^2-2)	\frac{d}{dx}(\frac{1}{x^{2}-2})
derivative of x^2+(128000/x)	\frac{d}{dx}(x^{2}+\frac{128000}{x})
area y=4-x^2,y=x^2-4x-2	area\:y=4-x^{2},y=x^{2}-4x-2
sum from n=2 to infinity of (3^n)/(10^n)	\sum\:_{n=2}^{\infty\:}\frac{3^{n}}{10^{n}}
taylor 1/(1+sin(pi*x))	taylor\:\frac{1}{1+\sin(π\cdot\:x)}
derivative of 1/(\sqrt[3]{(6x^2+5^2)})	\frac{d}{dx}(\frac{1}{\sqrt[3]{(6x^{2}+5)^{2}}})
integral of k/(xln(x))	\int\:\frac{k}{x\ln(x)}dx
derivative of sqrt(x/(x^2-8))	\frac{d}{dx}(\sqrt{\frac{x}{x^{2}-8}})
d/(d{x)}({y}{z}e^{{x}})	\frac{d}{d{x}}({y}{z}e^{{x}})
(dy)/(dx)=xy+2x+3y+6	\frac{dy}{dx}=xy+2x+3y+6
tangent of 7x^2,\at x=10	tangent\:7x^{2},\at\:x=10
y^{''}+4y^'+4y=6e^{-2x}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=6e^{-2x}
integral of 20x^4	\int\:20x^{4}dx
f^{''}(x)=7e^{-x}-8e^{-7x}	f^{\prime\:\prime\:}(x)=7e^{-x}-8e^{-7x}
integral of 3arcsin(3x)	\int\:3\arcsin(3x)dx
derivative of log_{5}(1+2x)	\frac{d}{dx}(\log_{5}(1+2x))
derivative of (x^{1/3}-4/(x^{7/2)})	\frac{d}{dx}(\frac{x^{\frac{1}{3}}-4}{x^{\frac{7}{2}}})
limit as x approaches 0 of x*cotan(2pix)	\lim\:_{x\to\:0}(x\cdot\:co\tan(2πx))
derivative of (x^2+x+1/x)	\frac{d}{dx}(\frac{x^{2}+x+1}{x})
y^{''}+9y=0	y^{\prime\:\prime\:}+9y=0
tangent of y=10cot((pix)/(20)),\at x=5	tangent\:y=10\cot(\frac{πx}{20}),\at\:x=5
derivative of (3+x{f}(x)/(sqrt(x)))	\frac{d}{dx}(\frac{3+x{f}(x)}{\sqrt{x}})
derivative of (arctan(4x))^2	derivative\:(\arctan(4x))^{2}

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