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Popular Calculus Problems

(dy)/(dx)y=x^x	\frac{dy}{dx}y=x^{x}
tangent of 8x^3-18x^2-6	tangent\:8x^{3}-18x^{2}-6
integral of-2x+18x^2-4x^3+16	\int\:-2x+18x^{2}-4x^{3}+16dx
limit as x approaches 3 of 4x^2-2x-6	\lim\:_{x\to\:3}(4x^{2}-2x-6)
normal of y=(sqrt(x))/(x+9),(1,0.1)	normal\:y=\frac{\sqrt{x}}{x+9},(1,0.1)
limit as x approaches infinity of-5x^2	\lim\:_{x\to\:\infty\:}(-5x^{2})
derivative of f(x)= 5/(x^2)+sin(x)	derivative\:f(x)=\frac{5}{x^{2}}+\sin(x)
x^'=0.1078*(1-x/(105900))x-x	x^{\prime\:}=0.1078\cdot\:(1-\frac{x}{105900})x-x
sum from n=1 to infinity of (15)/n	\sum\:_{n=1}^{\infty\:}\frac{15}{n}
integral from 0 to 1 of xe^{2x}	\int\:_{0}^{1}xe^{2x}dx
y^'+4y=6	y^{\prime\:}+4y=6
derivative of-6.25t^2+50t	derivative\:-6.25t^{2}+50t
(x^2+4xy)dx+xdy=0	(x^{2}+4xy)dx+xdy=0
limit as x approaches 1 of 5/((x-1)^2)	\lim\:_{x\to\:1}(\frac{5}{(x-1)^{2}})
derivative of (1+2x+3x^2+4x^3^{100})	\frac{d}{dx}((1+2x+3x^{2}+4x^{3})^{100})
inverse oflaplace (10)/((s-2)(s^3+s))	inverselaplace\:\frac{10}{(s-2)(s^{3}+s)}
2ty^'=4y	2ty^{\prime\:}=4y
(dP)/(dt)=0.08P(1-P/(1000))	\frac{dP}{dt}=0.08P(1-\frac{P}{1000})
integral of (x^2)/(sqrt((21+4x-x^2)))	\int\:\frac{x^{2}}{\sqrt{(21+4x-x^{2})}}dx
derivative of (d/(dx(e^x))/(1+x))	\frac{d}{dx}(\frac{\frac{d}{dx}(e^{x})}{1+x})
integral of 2x(8x^2-20)^2	\int\:2x(8x^{2}-20)^{2}dx
limit as x approaches 1+of 1+1/(x-1)	\lim\:_{x\to\:1+}(1+\frac{1}{x-1})
integral of sqrt(7x+5)	\int\:\sqrt{7x+5}dx
derivative of f(x)=sin(x^5)	derivative\:f(x)=\sin(x^{5})
limit as x approaches-2 of 1/((2+x)^3)	\lim\:_{x\to\:-2}(\frac{1}{(2+x)^{3}})
integral of 13xsin(x)	\int\:13x\sin(x)dx
y^'=y(xy^2+5)	y^{\prime\:}=y(xy^{2}+5)
integral of 3(sqrt(x))cos(x/3)	\int\:3(\sqrt{x})\cos(\frac{x}{3})dx
derivative of (x-1*sqrt(x^2-2x+2))	\frac{d}{dx}((x-1)\cdot\:\sqrt{x^{2}-2x+2})
integral of 2/(x^3+x^2)	\int\:\frac{2}{x^{3}+x^{2}}dx
d/(dy)(y^{2/3})	\frac{d}{dy}(y^{\frac{2}{3}})
derivative of y=(t^2+8)^2-2(t^2+8)	derivative\:y=(t^{2}+8)^{2}-2(t^{2}+8)
(\partial)/(\partial z)(e^{-x^2-2y^2-3z^2})	\frac{\partial\:}{\partial\:z}(e^{-x^{2}-2y^{2}-3z^{2}})
integral of (3x+1)^{11}	\int\:(3x+1)^{11}dx
integral from 0 to 6 of xe^{-x}	\int\:_{0}^{6}xe^{-x}dx
derivative of \sqrt[5]{ln(x^3+1})	\frac{d}{dx}(\sqrt[5]{\ln(x^{3}+1)})
derivative of ((sqrt(5x^4+x^2))/2)	\frac{d}{dx}(\frac{(\sqrt{5x^{4}+x^{2}})}{2})
(1+x^2)(1+y^2)dx-xydy=0	(1+x^{2})(1+y^{2})dx-xydy=0
integral of (6sin(3x)-cos(2x))	\int\:(6\sin(3x)-\cos(2x))dx
integral of x-4	\int\:x-4dx
limit as x approaches 0+of 3/(x^2-x)	\lim\:_{x\to\:0+}(\frac{3}{x^{2}-x})
integral of (16s+16)/((s^2+1)(s-1)^3)	\int\:\frac{16s+16}{(s^{2}+1)(s-1)^{3}}ds
limit as x approaches 0.999 of x^2+2	\lim\:_{x\to\:0.999}(x^{2}+2)
inverse oflaplace (2s)/(s^2+6)	inverselaplace\:\frac{2s}{s^{2}+6}
integral of (5/x-4/(x^5))	\int\:(\frac{5}{x}-\frac{4}{x^{5}})dx
(dy)/(dt)= 8/7 y	\frac{dy}{dt}=\frac{8}{7}y
(\partial)/(\partial x)((2x+3)(y-2))	\frac{\partial\:}{\partial\:x}((2x+3)(y-2))
tangent of y=x^3-3x+1	tangent\:y=x^{3}-3x+1
derivative of log_{3}(sin(x^2))	\frac{d}{dx}(\log_{3}(\sin(x^{2})))
limit as x approaches-2+of sqrt(2-x)	\lim\:_{x\to\:-2+}(\sqrt{2-x})
integral of x^2sqrt(x+5)	\int\:x^{2}\sqrt{x+5}dx
integral of iny	\int\:inydy
(1+x^4)(dy}{dx}=\frac{x^3)/y	(1+x^{4})\frac{dy}{dx}=\frac{x^{3}}{y}
integral of 3e^{(3t)/2}t	\int\:3e^{\frac{3t}{2}}tdt
tangent of f(x)=4x+6sqrt(x),\at x=4	tangent\:f(x)=4x+6\sqrt{x},\at\:x=4
tangent of f(x)=-3-4x^2,(5,-103)	tangent\:f(x)=-3-4x^{2},(5,-103)
tangent of f(x)=2x^3-x^2+1,\at x=2	tangent\:f(x)=2x^{3}-x^{2}+1,\at\:x=2
derivative of sin(x)-cos(x)	derivative\:\sin(x)-\cos(x)
x(dy)/(dx)+y=x^4ln(x)	x\frac{dy}{dx}+y=x^{4}\ln(x)
limit as x approaches 2+of (x+2)/(x^2-4)	\lim\:_{x\to\:2+}(\frac{x+2}{x^{2}-4})
derivative of sqrt(5+2x)	derivative\:\sqrt{5+2x}
integral of 1/(x^2sqrt(7-x^2))	\int\:\frac{1}{x^{2}\sqrt{7-x^{2}}}dx
(\partial}{\partial t}(\frac{(s-r))/t)	\frac{\partial\:}{\partial\:t}(\frac{(s-r)}{t})
limit as x approaches 10 of ((3x^2-30x))/(x^2-100)	\lim\:_{x\to\:10}(\frac{(3x^{2}-30x)}{x^{2}-100})
integral of (5x+1)/(2x^2-x-1)	\int\:\frac{5x+1}{2x^{2}-x-1}dx
derivative of 2xe^{-x}	derivative\:2xe^{-x}
derivative of 5/12 x^{6/5}-5/8 x^{4/5}	\frac{d}{dx}(\frac{5}{12}x^{\frac{6}{5}}-\frac{5}{8}x^{\frac{4}{5}})
(\partial)/(\partial y)(5x^2-2y)	\frac{\partial\:}{\partial\:y}(5x^{2}-2y)
inverse oflaplace 1/((s^2+9)^2)	inverselaplace\:\frac{1}{(s^{2}+9)^{2}}
derivative of (e^x-e^{-x}/(e^x+e^{-x)})	\frac{d}{dx}(\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}})
sum from n=1 to infinity of 9/(nln(2n))	\sum\:_{n=1}^{\infty\:}\frac{9}{n\ln(2n)}
(\partial)/(\partial y)(4ysin(x^2y))	\frac{\partial\:}{\partial\:y}(4y\sin(x^{2}y))
integral from 2 to 9 of 2/((1-x)^{2/3)}	\int\:_{2}^{9}\frac{2}{(1-x)^{\frac{2}{3}}}dx
integral from 0 to 5 of 2	\int\:_{0}^{5}2dx
integral of (2-x^2)^2	\int\:(2-x^{2})^{2}dx
derivative of sqrt(e^x+2)	\frac{d}{dx}(\sqrt{e^{x}+2})
((x+1)dy)/(dx)(x+1)y=2xe^{-x}	\frac{(x+1)dy}{dx}(x+1)y=2xe^{-x}
integral of (x^3)/((x^2+12)^3)	\int\:\frac{x^{3}}{(x^{2}+12)^{3}}dx
(dy)/(dx)= 1/(x^2y^2)	\frac{dy}{dx}=\frac{1}{x^{2}y^{2}}
maclaurin x^2e^{4x}	maclaurin\:x^{2}e^{4x}
(dy)/(dx)=e^{-ka*x},y(0)=0	\frac{dy}{dx}=e^{-ka\cdot\:x},y(0)=0
integral of (x^2-x+12)/(x^3+6x)	\int\:\frac{x^{2}-x+12}{x^{3}+6x}dx
(\partial)/(\partial x)(e^{3x}sin(cy))	\frac{\partial\:}{\partial\:x}(e^{3x}\sin(cy))
sum from n=0 to infinity of (3^n)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{2^{n}}
derivative of f(x)= 1/(2-3x)	derivative\:f(x)=\frac{1}{2-3x}
derivative of ln((1+sqrt(x)/(x^4)))	\frac{d}{dx}(\ln(\frac{1+\sqrt{x}}{x^{4}}))
sum from n=6 to infinity of (3^n)/(12^n)	\sum\:_{n=6}^{\infty\:}\frac{3^{n}}{12^{n}}
integral from 0 to 15 of sqrt(t+1)	\int\:_{0}^{15}\sqrt{t+1}dt
derivative of (1+x^3Y^2Z^2)	\frac{d}{dx}((1+x^{3}Y^{2}Z)^{2})
derivative of 4^xln(4)	\frac{d}{dx}(4^{x}\ln(4))
y^'(y-x^2)=-2y	y^{\prime\:}(y-x^{2})=-2y
(\partial)/(\partial x)(ln(x^4+y^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{4}+y^{2}))
y^'=7x+y,y(0)=8	y^{\prime\:}=7x+y,y(0)=8
area y=x^3,y=3x+2	area\:y=x^{3},y=3x+2
(\partial)/(\partial x)(2xy+y^3)	\frac{\partial\:}{\partial\:x}(2xy+y^{3})
integral from 0 to 1 of 1/(t+1)	\int\:_{0}^{1}\frac{1}{t+1}dt
implicit (dy)/(dx),xy=36	implicit\:\frac{dy}{dx},xy=36
(dy)/(dt)+2ty=2t	\frac{dy}{dt}+2ty=2t
integral of 1/(x^2(e^{1/x)-5)}	\int\:\frac{1}{x^{2}(e^{\frac{1}{x}}-5)}dx
integral of 1/2 x^2-2x+6	\int\:\frac{1}{2}x^{2}-2x+6dx

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