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Popular Calculus Problems

derivative of e^{-2t}	derivative\:e^{-2t}
derivative of xsqrt(5)	\frac{d}{dx}(x\sqrt{5})
sum from n=1 to infinity of ((-1))/n	\sum\:_{n=1}^{\infty\:}\frac{(-1)}{n}
inverse oflaplace s/((s^2+3^2)^2)	inverselaplace\:\frac{s}{(s^{2}+3^{2})^{2}}
sum from n=2 to infinity of 1/(4^n)	\sum\:_{n=2}^{\infty\:}\frac{1}{4^{n}}
integral from 0 to 1 of tsqrt(9t^2+4)	\int\:_{0}^{1}t\sqrt{9t^{2}+4}dt
inverse oflaplace x/(x+8)	inverselaplace\:\frac{x}{x+8}
integral of (cos(x))/x	\int\:\frac{\cos(x)}{x}dx
tangent of 5x^2-7x	tangent\:5x^{2}-7x
derivative of axe^{bx}	\frac{d}{dx}(a\cdot\:x\cdot\:e^{bx})
integral of (y-1)/(-y-1)	\int\:\frac{y-1}{-y-1}dy
(\partial)/(\partial y)(2(y+1)e^{2x})	\frac{\partial\:}{\partial\:y}(2(y+1)e^{2x})
slope ofintercept (-6,3),(4,-1)	slopeintercept\:(-6,3),(4,-1)
derivative of-19.6x+2	derivative\:-19.6x+2
integral of x\sqrt[4]{x+20}	\int\:x\sqrt[4]{x+20}dx
integral of 1/(sqrt(\sqrt{x)+1)}	\int\:\frac{1}{\sqrt{\sqrt{x}+1}}dx
(\partial)/(\partial y)(x^2-4xy+y^3+4y)	\frac{\partial\:}{\partial\:y}(x^{2}-4xy+y^{3}+4y)
integral of (2xyz+sin(x))	\int\:(2xyz+\sin(x))dx
derivative of x^4(x^2+1^6)	\frac{d}{dx}(x^{4}(x^{2}+1)^{6})
derivative of-5/((x+3^3))	\frac{d}{dx}(-\frac{5}{(x+3)^{3}})
taylor 1/((7+x)2)	taylor\:\frac{1}{(7+x)2}
limit as x approaches 0 of xsin(x)	\lim\:_{x\to\:0}(x\sin(x))
integral from 0 to ln(21) of xe^x	\int\:_{0}^{\ln(21)}xe^{x}dx
integral of 3/(x(x+3))	\int\:\frac{3}{x(x+3)}dx
integral of 1/(sqrt(12x-4x^2-8))	\int\:\frac{1}{\sqrt{12x-4x^{2}-8}}dx
derivative of 1-x^{2/3}	\frac{d}{dx}(1-x^{\frac{2}{3}})
derivative of 2x^7-7x^{-4}+2x^2-3x	\frac{d}{dx}(2x^{7}-7x^{-4}+2x^{2}-3x)
limit as x approaches infinity of (x+3)/(2x^3-5)	\lim\:_{x\to\:\infty\:}(\frac{x+3}{2x^{3}-5})
derivative of 3^xln(3)	derivative\:3^{x}\ln(3)
integral from 1 to 2 of 4r^2ln(r)	\int\:_{1}^{2}4r^{2}\ln(r)dr
derivative of (-9/(\sqrt[4]{x)})	\frac{d}{dx}(\frac{-9}{\sqrt[4]{x}})
derivative of ln((x-2/(x+1)))	\frac{d}{dx}(\ln(\frac{x-2}{x+1}))
integral of (2-x)^2ln(4x)	\int\:(2-x)^{2}\ln(4x)dx
derivative of 11/3 t^3+11t^2	derivative\:\frac{11}{3}t^{3}+11t^{2}
derivative of (6x^2+6e^{-x})	\frac{d}{dx}((6x^{2}+6)e^{-x})
derivative of e^{ln(2})	\frac{d}{dx}(e^{\ln(2)})
tangent of y=3x^3-3x,(-1,0)	tangent\:y=3x^{3}-3x,(-1,0)
(\partial}{\partial t}(\frac{(r+s))/t)	\frac{\partial\:}{\partial\:t}(\frac{(r+s)}{t})
derivative of f(x)=4x^3sqrt(x^4)	derivative\:f(x)=4x^{3}\sqrt{x^{4}}
derivative of (xsin(4x)/8)	\frac{d}{dx}(\frac{x\sin(4x)}{8})
6y^{''}+4y^'+7y=0	6y^{\prime\:\prime\:}+4y^{\prime\:}+7y=0
tangent of f(x)=2x^2+x-1	tangent\:f(x)=2x^{2}+x-1
y^{''}+9y=0,y(pi/2)=1,y^'(pi/2)=-3	y^{\prime\:\prime\:}+9y=0,y(\frac{π}{2})=1,y^{\prime\:}(\frac{π}{2})=-3
implicit (dy)/(dx),9y+x=4y	implicit\:\frac{dy}{dx},9y+x=4y
integral of (6x^2-4e^x)	\int\:(6x^{2}-4e^{x})dx
derivative of (5x^3+5x^2)/x	derivative\:\frac{5x^{3}+5x^{2}}{x}
integral of (arctan(sqrt(x)))/(x^2)	\int\:\frac{\arctan(\sqrt{x})}{x^{2}}dx
area x=4y^2,x+y=3	area\:x=4y^{2},x+y=3
integral of (10x)/(81x^4+49)	\int\:\frac{10x}{81x^{4}+49}dx
integral of arccos(x)	\int\:\arccos(x)dx
integral of cos^7(5x)\sqrt[5]{sin(5x)}	\int\:\cos^{7}(5x)\sqrt[5]{\sin(5x)}dx
integral from-2 to 2 of (x^3-1)	\int\:_{-2}^{2}(x^{3}-1)dx
(\partial)/(\partial x)(x^3+x^2y^3-2y^2)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}y^{3}-2y^{2})
derivative of f(x)=(6x^2-9x)e^x	derivative\:f(x)=(6x^{2}-9x)e^{x}
derivative of ((x^2)/(x^2+1))	\frac{d}{dx}(\frac{(x^{2})}{x^{2}+1})
sum from n=1 to infinity of (1/6)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{6})^{n}
tangent of x^2+8x-7	tangent\:x^{2}+8x-7
derivative of (9x)/(2^x)	derivative\:\frac{9x}{2^{x}}
derivative of y=sqrt(4x^2+2)	derivative\:y=\sqrt{4x^{2}+2}
limit as x approaches-2 of (x^2-3)/(x+2)	\lim\:_{x\to\:-2}(\frac{x^{2}-3}{x+2})
(\partial)/(\partial y)(e^{x^2-y})	\frac{\partial\:}{\partial\:y}(e^{x^{2}-y})
integral of 3sqrt(x)+(10)/(x^6)	\int\:3\sqrt{x}+\frac{10}{x^{6}}dx
(d^2)/(dx^2)(log_{10}(x))	\frac{d^{2}}{dx^{2}}(\log_{10}(x))
derivative of (5x)^{1/3}	derivative\:(5x)^{\frac{1}{3}}
derivative of (-4x^5-2pi^2/(x^7))	\frac{d}{dx}(\frac{-4x^{5}-2π^{2}}{x^{7}})
integral of 1-cos(2x)	\int\:1-\cos(2x)dx
inverse oflaplace 1/(s^2+2s)	inverselaplace\:\frac{1}{s^{2}+2s}
integral of u^6	\int\:u^{6}du
limit as x approaches 5 of sin((pix)/3)	\lim\:_{x\to\:5}(\sin(\frac{πx}{3}))
(3x^2-2xy)dx+(2y-x^2)dy=0	(3x^{2}-2xy)dx+(2y-x^{2})dy=0
integral from-1 to 3 of (x^2-2x)	\int\:_{-1}^{3}(x^{2}-2x)dx
integral from 0 to 3 of 9/(x^2+9)	\int\:_{0}^{3}\frac{9}{x^{2}+9}dx
integral of 5picos(pi)x	\int\:5π\cos(π)xdx
integral of (x^{1.7}+11x^{4.5})	\int\:(x^{1.7}+11x^{4.5})dx
y^'=(18(1+3y))/((3-3x)^2),y(2)=0	y^{\prime\:}=\frac{18(1+3y)}{(3-3x)^{2}},y(2)=0
derivative of \sqrt[3]{x}+3/x	\frac{d}{dx}(\sqrt[3]{x}+\frac{3}{x})
integral from-4 to 2 of 12-x-x^2-(x+4)	\int\:_{-4}^{2}12-x-x^{2}-(x+4)dx
(\partial)/(\partial x)(9ln(8x^2+y^3))	\frac{\partial\:}{\partial\:x}(9\ln(8x^{2}+y^{3}))
derivative of (2x+1^3\sqrt[4]{(3x-1)^5})	\frac{d}{dx}((2x+1)^{3}\sqrt[4]{(3x-1)^{5}})
integral of e^{8x}sin(x)	\int\:e^{8x}\sin(x)dx
(\partial)/(\partial x)(x^2sin(1/x))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(\frac{1}{x}))
taylor 1/(x(x+1))	taylor\:\frac{1}{x(x+1)}
integral of (3x^2+4x+1)/(3x^3+6x^2+3x+5)	\int\:\frac{3x^{2}+4x+1}{3x^{3}+6x^{2}+3x+5}dx
derivative of y=x^2sin^6(x)+xcos^{-4}(x)	derivative\:y=x^{2}\sin^{6}(x)+x\cos^{-4}(x)
derivative of (x-1/(x^2+1))	\frac{d}{dx}(\frac{x-1}{x^{2}+1})
derivative of (3x^4/4)	\frac{d}{dx}(\frac{3x^{4}}{4})
integral of (2x-1)/(x^2-x-12)	\int\:\frac{2x-1}{x^{2}-x-12}dx
y^{''}+9y=5e^x-162x	y^{\prime\:\prime\:}+9y=5e^{x}-162x
integral of-(x^3)/3-x^2+4/3	\int\:-\frac{x^{3}}{3}-x^{2}+\frac{4}{3}dx
derivative of 2arcsin(x/2)	\frac{d}{dx}(2\arcsin(\frac{x}{2}))
(dy)/(dx)=7xsqrt(5y+11),y(0)=9	\frac{dy}{dx}=7x\sqrt{5y+11},y(0)=9
derivative of f(x)=\sqrt[5]{x}	derivative\:f(x)=\sqrt[5]{x}
(dy)/(dx)-xy=0	\frac{dy}{dx}-xy=0
(dy)/(dx)=2cos(x)y^3	\frac{dy}{dx}=2\cos(x)y^{3}
integral from-2 to 3 of (47)/(x^4)	\int\:_{-2}^{3}\frac{47}{x^{4}}dx
(\partial)/(\partial t)(ln(t^2+1))	\frac{\partial\:}{\partial\:t}(\ln(t^{2}+1))
derivative of 1/(6x)	derivative\:\frac{1}{6x}
derivative of (3x/(x^2+1))	\frac{d}{dx}(\frac{3x}{x^{2}+1})
integral of xsin(15-x)	\int\:x\sin(15-x)dx
integral of 1/(cos(2x))	\int\:\frac{1}{\cos(2x)}dx

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