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Popular Calculus Problems

derivative of x/2	derivative\:\frac{x}{2}
limit as x approaches 0 of x^{11x}	\lim\:_{x\to\:0}(x^{11x})
(dP)/(dt)=(9/240)P-1/4800 (P)^2	\frac{dP}{dt}=(\frac{9}{240})P-\frac{1}{4800}(P)^{2}
x(dy)/(dx)+y-y^2e^{2x}=0	x\frac{dy}{dx}+y-y^{2}e^{2x}=0
limit as x approaches 0 of sin(x)*ln(x)	\lim\:_{x\to\:0}(\sin(x)\cdot\:\ln(x))
integral of 4tan^2(x)+tan^4(x)	\int\:4\tan^{2}(x)+\tan^{4}(x)dx
derivative of y=ln(e^{2x})	derivative\:y=\ln(e^{2x})
(\partial)/(\partial x)(arctan(t/x))	\frac{\partial\:}{\partial\:x}(\arctan(\frac{t}{x}))
integral of (4x+3)sqrt(2x^2+3x)	\int\:(4x+3)\sqrt{2x^{2}+3x}dx
y^'=e^y*5^x	y^{\prime\:}=e^{y}\cdot\:5^{x}
limit as x approaches 0 of (e^x)/x	\lim\:_{x\to\:0}(\frac{e^{x}}{x})
(\partial)/(\partial x)(-4y^2x(6-x^2y^2))	\frac{\partial\:}{\partial\:x}(-4y^{2}x(6-x^{2}y^{2}))
(x^2+1)*(dy)/(dx)+3x(y-1)=0	(x^{2}+1)\cdot\:\frac{dy}{dx}+3x(y-1)=0
limit as x approaches 5 of 3x+2	\lim\:_{x\to\:5}(3x+2)
y^{''}-6y^'-7y=0	y^{\prime\:\prime\:}-6y^{\prime\:}-7y=0
slope of (-40)(-4-10)	slope\:(-40)(-4-10)
tangent of 6x-32sqrt(x)	tangent\:6x-32\sqrt{x}
(\partial)/(\partial x)((5x)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{5x}{x^{2}+y^{2}})
f(x)=2^xln(2)	f(x)=2^{x}\ln(2)
integral of sqrt(2/x)	\int\:\sqrt{\frac{2}{x}}dx
sum from n=0 to infinity of 1/(n+15)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+15}
integral from 0 to 0.1 of f(10t)	\int\:_{0}^{0.1}f(10t)dt
integral of (ln(x))^0	\int\:(\ln(x))^{0}dx
integral of 1/(x^2sqrt(5-x^2))	\int\:\frac{1}{x^{2}\sqrt{5-x^{2}}}dx
integral of (6sin(2x)-3cos(3x))	\int\:(6\sin(2x)-3\cos(3x))dx
integral of 18cos^5(x)sin(x)	\int\:18\cos^{5}(x)\sin(x)dx
derivative of (2x+1)^{-2}	derivative\:(2x+1)^{-2}
integral of x^{8/9}	\int\:x^{\frac{8}{9}}dx
(\partial)/(\partial x)((2xy^2)/(3+x^2y^2))	\frac{\partial\:}{\partial\:x}(\frac{2xy^{2}}{3+x^{2}y^{2}})
slope of (12,11),(9,5)	slope\:(12,11),(9,5)
derivative of 3/((3-x^2))	\frac{d}{dx}(\frac{3}{(3-x)^{2}})
integral from 0 to 9 of pi(sqrt(x))^2	\int\:_{0}^{9}π(\sqrt{x})^{2}dx
2^{(2-x^4)}	2^{(2-x^{4})}
derivative of (3x^3+4(x^4-3x))	\frac{d}{dx}((3x^{3}+4)(x^{4}-3x))
tangent of f(x)= 7/x ,\at x=2	tangent\:f(x)=\frac{7}{x},\at\:x=2
integral from 1 to 18 of sqrt(3/z)	\int\:_{1}^{18}\sqrt{\frac{3}{z}}dz
derivative of-x+7x^2-15x	derivative\:-x+7x^{2}-15x
y^'=7y^2+xy^2,y(0)=1	y^{\prime\:}=7y^{2}+xy^{2},y(0)=1
integral of (x^2-6x+9)/(sqrt(x^2-6x+18))	\int\:\frac{x^{2}-6x+9}{\sqrt{x^{2}-6x+18}}dx
integral of 1/(x^3+27)	\int\:\frac{1}{x^{3}+27}dx
limit as x approaches 0 of (x-4)/(x-4)	\lim\:_{x\to\:0}(\frac{x-4}{x-4})
integral of sin(2x)(e^{cos(x)})	\int\:\sin(2x)(e^{\cos(x)})dx
integral of arccosh(x)	\int\:\arccosh(x)dx
8y^'+y=6t^2	8y^{\prime\:}+y=6t^{2}
integral of sqrt(1+3x)	\int\:\sqrt{1+3x}dx
derivative of y=cos(x^2)2x	derivative\:y=\cos(x^{2})2x
sum from n=1 to infinity}((e^{8/n of))/n	\sum\:_{n=1}^{\infty\:}\frac{(e^{\frac{8}{n}})}{n}
derivative of ((x-7/(x-9))^4)	\frac{d}{dx}((\frac{x-7}{x-9})^{4})
integral of (ln(20x))/x	\int\:\frac{\ln(20x)}{x}dx
d/(dy)(-e^y)	\frac{d}{dy}(-e^{y})
(d^2y)/(dx^2)+16y=0	\frac{d^{2}y}{dx^{2}}+16y=0
derivative of f(x)=-x^3+2x-e^{-x}-3	derivative\:f(x)=-x^{3}+2x-e^{-x}-3
inverse oflaplace 3/(\frac{s+2){s}}	inverselaplace\:\frac{3}{\frac{s+2}{s}}
(\partial)/(\partial x)(2x^4+5y^2+xy)	\frac{\partial\:}{\partial\:x}(2x^{4}+5y^{2}+xy)
integral of 3/x+10sec^2(x)+40e^x	\int\:\frac{3}{x}+10\sec^{2}(x)+40e^{x}dx
derivative of e^{xy}cos(x+y)	\frac{d}{dx}(e^{xy}\cos(x+y))
y^'-3/(x^2)y= 1/(x^2)	y^{\prime\:}-\frac{3}{x^{2}}y=\frac{1}{x^{2}}
y^'= t/(t^2y+y)	y^{\prime\:}=\frac{t}{t^{2}y+y}
sum from n=1 to infinity of ne^{-n/8}	\sum\:_{n=1}^{\infty\:}ne^{-\frac{n}{8}}
y^{''}+20y^'=0,y(0)=-5,y^'(0)=20	y^{\prime\:\prime\:}+20y^{\prime\:}=0,y(0)=-5,y^{\prime\:}(0)=20
(d^2)/(dx^2)(x^{1/11})	\frac{d^{2}}{dx^{2}}(x^{\frac{1}{11}})
(\partial)/(\partial x)(xe^{x^2+y^2})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}+y^{2}})
(\partial)/(\partial x)((e^v)/(u(v,x)+v^2))	\frac{\partial\:}{\partial\:x}(\frac{e^{v}}{u(v,x)+v^{2}})
(e^x)^'	(e^{x})^{\prime\:}
derivative of f(x)=x^5+1/(x^5)	derivative\:f(x)=x^{5}+\frac{1}{x^{5}}
integral of 2/(x^3)+3/(x^2)+5	\int\:\frac{2}{x^{3}}+\frac{3}{x^{2}}+5dx
x^{''}+x^'=0	x^{\prime\:\prime\:}+x^{\prime\:}=0
derivative of x^2arctan(5x)	derivative\:x^{2}\arctan(5x)
integral of e^{(4x)/9}(4/9)	\int\:e^{\frac{4x}{9}}(\frac{4}{9})dx
tangent of x^2-4x	tangent\:x^{2}-4x
derivative of log_{10}(7x)	\frac{d}{dx}(\log_{10}(7x))
integral of sin(1/10)xsin(1/20)x	\int\:\sin(\frac{1}{10})x\sin(\frac{1}{20})xdx
limit as x approaches 4+of 5x^2+x	\lim\:_{x\to\:4+}(5x^{2}+x)
3x(dy)/(dx)=2xe^x-3y+6x^2	3x\frac{dy}{dx}=2xe^{x}-3y+6x^{2}
integral of (8-5x)/(x^2-12x-32)	\int\:\frac{8-5x}{x^{2}-12x-32}dx
integral of t/((t^2+1)^{13/2)}	\int\:\frac{t}{(t^{2}+1)^{\frac{13}{2}}}dt
limit as x approaches 0 of (tan(2x))/x	\lim\:_{x\to\:0}(\frac{\tan(2x)}{x})
(\partial)/(\partial x)(cos(4y-2x))	\frac{\partial\:}{\partial\:x}(\cos(4y-2x))
x^'=2-x,x(5)=4	x^{\prime\:}=2-x,x(5)=4
limit as x approaches 0 of (x^4)cos(2/x)	\lim\:_{x\to\:0}((x^{4})\cos(\frac{2}{x}))
xy^'=(1-x)y+x^2+x^3,y(3)=2	xy^{\prime\:}=(1-x)y+x^{2}+x^{3},y(3)=2
integral of cos^2(xsi)n^4x	\int\:\cos^{2}(xsi)n^{4}xdx
integral of 60x^9sin(3x^{10})	\int\:60x^{9}\sin(3x^{10})dx
tangent of sqrt(3x+1),\at x=5	tangent\:\sqrt{3x+1},\at\:x=5
(\partial)/(\partial x)(e^x-1)	\frac{\partial\:}{\partial\:x}(e^{x}-1)
derivative of 1/(5x^{4/5})	\frac{d}{dx}(\frac{1}{5x^{\frac{4}{5}}})
integral of sqrt(w)	\int\:\sqrt{w}dw
integral of x^3+2x	\int\:x^{3}+2xdx
(dy)/(dx)=1-x-y	\frac{dy}{dx}=1-x-y
tangent of f(x)=-8x^2+5x,\at x=-1	tangent\:f(x)=-8x^{2}+5x,\at\:x=-1
integral of 5x+c	\int\:5x+cdx
area y=sqrt(25-x^2),y=0	area\:y=\sqrt{25-x^{2}},y=0
integral of sqrt(1+2x^2)(4x)	\int\:\sqrt{1+2x^{2}}(4x)dx
integral of (sqrt(x^2-5))/x	\int\:\frac{\sqrt{x^{2}-5}}{x}dx
(\partial)/(\partial x)(2y^2)	\frac{\partial\:}{\partial\:x}(2y^{2})
derivative of 2^{1/2}	\frac{d}{dx}(2^{\frac{1}{2}})
integral of tan^6(x)sec^4(x)	\int\:\tan^{6}(x)\sec^{4}(x)dx
derivative of 4^{(x^9})	\frac{d}{dx}(4^{(x^{9})})
integral of (2x^2-1)^2	\int\:(2x^{2}-1)^{2}dx
(\partial)/(\partial x)(e^{-2x}cos(piy))	\frac{\partial\:}{\partial\:x}(e^{-2x}\cos(πy))

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