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Popular Calculus Problems

x^2e^x+4ye^{(-y)}y^'=0	x^{2}\cdot\:e^{x}+4\cdot\:y\cdot\:e^{(-y)}\cdot\:y^{\prime\:}=0
derivative of (x-1ln(x-1))	\frac{d}{dx}((x-1)\ln(x-1))
integral from 0 to x^2 of t^2	\int\:_{0}^{x^{2}}t^{2}dt
derivative of y=5x^4-x^2+6	derivative\:y=5x^{4}-x^{2}+6
derivative of 2x+9	\frac{d}{dx}(2x+9)
integral of (4x^3+2x^2+1)/(4x^3-x)	\int\:\frac{4x^{3}+2x^{2}+1}{4x^{3}-x}dx
derivative of (x^3+6)e^x	derivative\:(x^{3}+6)e^{x}
derivative of log_{3}(4x-3)	\frac{d}{dx}(\log_{3}(4x-3))
integral of cot^3(x/2)csc^4(x/2)	\int\:\cot^{3}(\frac{x}{2})\csc^{4}(\frac{x}{2})dx
tangent of f(x)=5e^x,\at x=4	tangent\:f(x)=5e^{x},\at\:x=4
integral of (sin(2x))^3	\int\:(\sin(2x))^{3}dx
integral of (1/(x^3+1))	\int\:(\frac{1}{x^{3}+1})dx
derivative of x(2x+1)^3	derivative\:x(2x+1)^{3}
derivative of sinh^2(3x+arcsin(2x))	\frac{d}{dx}(\sinh^{2}(3x)+\arcsin(2x))
integral of (3x^3+(2x-3)^2)	\int\:(3x^{3}+(2x-3)^{2})dx
derivative of sqrt(tan(x+cot(x)))	\frac{d}{dx}(\sqrt{\tan(x)+\cot(x)})
(\partial)/(\partial x)(sqrt(x^2+4xy+y^6))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+4xy+y^{6}})
derivative of x/(2^x)	\frac{d}{dx}(\frac{x}{2^{x}})
integral from 1 to e of x^nln(x^m)	\int\:_{1}^{e}x^{n}\ln(x^{m})dx
(d^2)/(dx^2)(e^{6e^x})	\frac{d^{2}}{dx^{2}}(e^{6e^{x}})
f(x)=x^4-4x^3-20x^2+96x+60	f(x)=x^{4}-4x^{3}-20x^{2}+96x+60
y^{''}+3y^'=0,y(0)=2	y^{\prime\:\prime\:}+3y^{\prime\:}=0,y(0)=2
integral of cos^2(xsi)n^2x	\int\:\cos^{2}(xsi)n^{2}xdx
(dx)/(dy)=((x^2y^2))/(1+x)	\frac{dx}{dy}=\frac{(x^{2}y^{2})}{1+x}
limit as x approaches 0 of (x)^{sin(x)}	\lim\:_{x\to\:0}((x)^{\sin(x)})
inverse oflaplace (1960)/(s^2+196)	inverselaplace\:\frac{1960}{s^{2}+196}
y^'=-3y+2e^{-x}	y^{\prime\:}=-3y+2e^{-x}
slope ofintercept (4,-2),(-8,-1)	slopeintercept\:(4,-2),(-8,-1)
limit as x approaches 3 of sqrt(25-x^2)	\lim\:_{x\to\:3}(\sqrt{25-x^{2}})
derivative of y=sin(tan(6x))	derivative\:y=\sin(\tan(6x))
(\partial)/(\partial y)(xy+ln(y)+2x^2)	\frac{\partial\:}{\partial\:y}(xy+\ln(y)+2x^{2})
(\partial)/(\partial x)(cos^3(x)y-1)	\frac{\partial\:}{\partial\:x}(\cos^{3}(x)y-1)
inverse oflaplace (s^2)/((s^2+4)^2)	inverselaplace\:\frac{s^{2}}{(s^{2}+4)^{2}}
(2y+3x)dx=-xdy	(2y+3x)dx=-xdy
derivative of (12/(x^2))	\frac{d}{dx}(\frac{12}{x^{2}})
y^{''}+y^'+3y=3t^2	y^{\prime\:\prime\:}+y^{\prime\:}+3y=3t^{2}
integral of (sqrt(49x^2-1))/x	\int\:\frac{\sqrt{49x^{2}-1}}{x}dx
integral of \sqrt[8]{x^9}	\int\:\sqrt[8]{x^{9}}dx
x^2y^{''}+xy^'-y=0	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}-y=0
derivative of (3x+1^2)	\frac{d}{dx}((3x+1)^{2})
derivative of (e^{2-3x}/(x^2))	\frac{d}{dx}(\frac{e^{2-3x}}{x^{2}})
derivative of ((s^2-4s+20))/((s+2)(s+4))	derivative\:\frac{(s^{2}-4s+20)}{(s+2)(s+4)}
integral of (6e^{-0.1x})	\int\:(6e^{-0.1x})dx
derivative of (x^2+2x-3/((x+1)^2))	\frac{d}{dx}(\frac{x^{2}+2x-3}{(x+1)^{2}})
limit as x approaches-4 of (x^2-6)/(4-x)	\lim\:_{x\to\:-4}(\frac{x^{2}-6}{4-x})
derivative of (x^3+3x(2x+4))	\frac{d}{dx}((x^{3}+3x)(2x+4))
integral of ysqrt(y)	\int\:y\sqrt{y}dy
(dy)/(dx)=x(5-y)	\frac{dy}{dx}=x(5-y)
limit as x approaches infinity of 3/x	\lim\:_{x\to\:\infty\:}(\frac{3}{x})
sum from n=0 to infinity of 1-(2/3)^n	\sum\:_{n=0}^{\infty\:}1-(\frac{2}{3})^{n}
limit as x approaches 4 of x^2+2x+2	\lim\:_{x\to\:4}(x^{2}+2x+2)
derivative of (sqrt(-x+y-2)/(x-2))	\frac{d}{dx}(\frac{\sqrt{-x+y-2}}{x-2})
derivative of log_{2}((x^2/(x-1)))	\frac{d}{dx}(\log_{2}(\frac{x^{2}}{x-1}))
limit as x approaches+3 of (pi+x)/4	\lim\:_{x\to\:+3}(\frac{π+x}{4})
d/(dθ)(sin(θ)+csc(θ))	\frac{d}{dθ}(\sin(θ)+\csc(θ))
limit as x approaches pi/2 of 5sec(x)	\lim\:_{x\to\:\frac{π}{2}}(5\sec(x))
derivative of (x^3y-xy^3/(x^2+y^2))	\frac{d}{dx}(\frac{x^{3}y-xy^{3}}{x^{2}+y^{2}})
(\partial)/(\partial x)(z^3x^2e^{zx}+x^2z)	\frac{\partial\:}{\partial\:x}(z^{3}x^{2}e^{zx}+x^{2}z)
y^'(y-x)=1	y^{\prime\:}(y-x)=1
integral of-x*ln(x)	\int\:-x\cdot\:\ln(x)dx
integral of 1/(1+16x^2)	\int\:\frac{1}{1+16x^{2}}dx
integral from-1 to 2 of (-y^2+y+2)	\int\:_{-1}^{2}(-y^{2}+y+2)dy
derivative of x^3cos(x^2)	derivative\:x^{3}\cos(x^{2})
integral of (x^2)/(sqrt(25-9x^2))	\int\:\frac{x^{2}}{\sqrt{25-9x^{2}}}dx
2y^{''}-9y^'-5y=0	2y^{\prime\:\prime\:}-9y^{\prime\:}-5y=0
derivative of sec^2(pix)	derivative\:\sec^{2}(πx)
derivative of 6/(x+2)	\frac{d}{dx}(\frac{6}{x+2})
tangent of f(x)=(2+3x)(6-5x),\at x=1	tangent\:f(x)=(2+3x)(6-5x),\at\:x=1
derivative of e^{(3-x})	\frac{d}{dx}(e^{(3-x)})
derivative of xe^{-3x}	\frac{d}{dx}(xe^{-3x})
integral of cos(x)(4+4sin^2(x))	\int\:\cos(x)(4+4\sin^{2}(x))dx
limit as x approaches 0 of (x-x)/(x^2)	\lim\:_{x\to\:0}(\frac{x-x}{x^{2}})
derivative of (x+1ln^2(x+1))	\frac{d}{dx}((x+1)\ln^{2}(x+1))
derivative of y=x(x^2+1)	derivative\:y=x(x^{2}+1)
f(y)=cos^2(y)	f(y)=\cos^{2}(y)
integral of sec^4(5x)tan^3(5x)	\int\:\sec^{4}(5x)\tan^{3}(5x)dx
f^'(x)= 1/(1+\frac{1){1+1/(1+x)}}	f^{\prime\:}(x)=\frac{1}{1+\frac{1}{1+\frac{1}{1+x}}}
derivative of (x^3)/(1-x^2)	derivative\:\frac{x^{3}}{1-x^{2}}
integral of \sqrt[3]{x}(x+1)^2	\int\:\sqrt[3]{x}(x+1)^{2}dx
integral of ((3x^2+2)/(x^2))	\int\:(\frac{3x^{2}+2}{x^{2}})dx
area f(x)=xsin(x),0,2pi	area\:f(x)=x\sin(x),0,2π
derivative of (-3x+2^4(-2x+3)^3)	\frac{d}{dx}((-3x+2)^{4}(-2x+3)^{3})
derivative of f(x)=sqrt(x-5)	derivative\:f(x)=\sqrt{x-5}
y^{''}+2y^'+y=sin(x)+4cos(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+y=\sin(x)+4\cos(2x)
(y+4)*(dy)/(dx)=2xy+4y	(y+4)\cdot\:\frac{dy}{dx}=2xy+4y
limit as x approaches pi of-csc(2x)	\lim\:_{x\to\:π}(-\csc(2x))
integral of sec(2x)+tan(2x)	\int\:\sec(2x)+\tan(2x)dx
limit as x approaches 1 of ln(2x)+e^x	\lim\:_{x\to\:1}(\ln(2x)+e^{x})
inverse oflaplace (11)/((s-1)^3)	inverselaplace\:\frac{11}{(s-1)^{3}}
integral from 0 to 2 of 8x-1/8 x	\int\:_{0}^{2}8x-\frac{1}{8}xdx
sum from n=0 to infinity of 2x^{2n}	\sum\:_{n=0}^{\infty\:}2x^{2n}
integral from 3 to infinity of e^{-x}	\int\:_{3}^{\infty\:}e^{-x}dx
limit as x approaches 3+of 3/(x^2-9)	\lim\:_{x\to\:3+}(\frac{3}{x^{2}-9})
integral from 0 to 0.9 of 1/(1-x)	\int\:_{0}^{0.9}\frac{1}{1-x}dx
8y^{''}+2y^'-y=0	8y^{\prime\:\prime\:}+2y^{\prime\:}-y=0
area sin(x),cos(x),[0, pi/2 ]	area\:\sin(x),\cos(x),[0,\frac{π}{2}]
(dy)/(dx)=2xe^{4y}	\frac{dy}{dx}=2xe^{4y}
y^{''}-2y^'+y=-6-3x+(2e^x)/x	y^{\prime\:\prime\:}-2y^{\prime\:}+y=-6-3x+\frac{2e^{x}}{x}
derivative of ln(sqrt(x^2e^{x^{2+1)}})	\frac{d}{dx}(\ln(\sqrt{x^{2}e^{x^{2+1}}}))
integral of cot^5(x)csc^2(x)	\int\:\cot^{5}(x)\csc^{2}(x)dx

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