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Popular Calculus Problems

(\partial)/(\partial y)(sin(x^2y))	\frac{\partial\:}{\partial\:y}(\sin(x^{2}y))
derivative of (x^3+6x^4)	\frac{d}{dx}((x^{3}+6x)^{4})
inverse oflaplace (2e^{-2s})/(3s^2+12)	inverselaplace\:\frac{2e^{-2s}}{3s^{2}+12}
3y^'+y=6t,y(0)=3	3y^{\prime\:}+y=6t,y(0)=3
derivative of sqrt(6x+5)	\frac{d}{dx}(\sqrt{6x+5})
(dy)/(dx)=4x^3	\frac{dy}{dx}=4x^{3}
tangent of f(x)=-5cos(x),\at x= pi/2	tangent\:f(x)=-5\cos(x),\at\:x=\frac{π}{2}
integral of 3/x+2/(x^2)	\int\:\frac{3}{x}+\frac{2}{x^{2}}dx
(dy)/(dx)=((x-1))/((y-4))	\frac{dy}{dx}=\frac{(x-1)}{(y-4)}
integral from 2 to infinity of 3/(x^2-x)	\int\:_{2}^{\infty\:}\frac{3}{x^{2}-x}dx
area y=x^3-x,y=7x-x^3	area\:y=x^{3}-x,y=7x-x^{3}
(\partial)/(\partial y)(6ln(6x^3+y^2))	\frac{\partial\:}{\partial\:y}(6\ln(6x^{3}+y^{2}))
derivative of ln^2(x-ln(ln(x)))	\frac{d}{dx}(\ln^{2}(x)-\ln(\ln(x)))
implicit (dy)/(dx),e^{x/y}=4x-y	implicit\:\frac{dy}{dx},e^{\frac{x}{y}}=4x-y
integral from 0 to 4 of (2-sqrt(x))^2	\int\:_{0}^{4}(2-\sqrt{x})^{2}dx
sum from n=0 to infinity of 1/(n+14)	\sum\:_{n=0}^{\infty\:}\frac{1}{n+14}
integral of t+2+3/(t^2+1)	\int\:t+2+\frac{3}{t^{2}+1}dt
derivative of (-8x^7+7x^3-2/(-4x^3))	\frac{d}{dx}(\frac{-8x^{7}+7x^{3}-2}{-4x^{3}})
integral of (ax+b+x^2)^2	\int\:(ax+b+x^{2})^{2}dx
derivative of (7-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{7-\sec(x)}{\tan(x)})
derivative of (-x^2+4x+5(4x^4-3))	\frac{d}{dx}((-x^{2}+4x+5)(4x^{4}-3))
(dy}{dx}-\frac{2y)/x =x^2-1	\frac{dy}{dx}-\frac{2y}{x}=x^{2}-1
integral of 1/2 x	\int\:\frac{1}{2}xdx
integral of 1+9/(x^2-4)	\int\:1+\frac{9}{x^{2}-4}dx
derivative of x^2e^{-x}	derivative\:x^{2}e^{-x}
integral from-pi to pi of sin(mx)sin(nx)	\int\:_{-π}^{π}\sin(mx)\sin(nx)dx
(y^2+4)dx-1/((2x+5)^2)dy=0	(y^{2}+4)dx-\frac{1}{(2x+5)^{2}}dy=0
integral from 0 to 1 of (x^2)/(25+x^2)	\int\:_{0}^{1}\frac{x^{2}}{25+x^{2}}dx
integral of 3/(t^4)cos(1/(t^3)-9)	\int\:\frac{3}{t^{4}}\cos(\frac{1}{t^{3}}-9)dt
integral from-8 to 8 of 1/2 (64-x^2)	\int\:_{-8}^{8}\frac{1}{2}(64-x^{2})dx
sum from n=1 to infinity of 8/(n^4)	\sum\:_{n=1}^{\infty\:}\frac{8}{n^{4}}
y^'sin(x)+ycos(x)=0	y^{\prime\:}\sin(x)+y\cos(x)=0
derivative of 147.456pit	derivative\:147.456πt
(\partial)/(\partial x)(x^2y^3+2xy^{-3}+5x+3y+11)	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}+2xy^{-3}+5x+3y+11)
limit as t approaches 5 of 1/(t^2-4t-5)-1/(6(t-5))	\lim\:_{t\to\:5}(\frac{1}{t^{2}-4t-5}-\frac{1}{6(t-5)})
sum from n=0 to infinity of (x^n)/(n+2)	\sum\:_{n=0}^{\infty\:}\frac{x^{n}}{n+2}
limit as x approaches 0 of 8/(1+sin(x))	\lim\:_{x\to\:0}(\frac{8}{1+\sin(x)})
derivative of (log_{5}(x))/(6+x^5)	derivative\:\frac{\log_{5}(x)}{6+x^{5}}
(\partial)/(\partial x)(ycos(y-2x))	\frac{\partial\:}{\partial\:x}(y\cos(y-2x))
integral of (-y)/y	\int\:\frac{-y}{y}dy
y^'+2x(y+1)=0	y^{\prime\:}+2x(y+1)=0
integral from-1 to 1 of 2xsin(1-x^2)	\int\:_{-1}^{1}2x\sin(1-x^{2})dx
inverse oflaplace x^{2+6x}	inverselaplace\:x^{2+6x}
integral of (cos(2x)-3)/(cos(2x))	\int\:\frac{\cos(2x)-3}{\cos(2x)}dx
integral of 1/10 e^{-x/(10)}	\int\:\frac{1}{10}e^{-\frac{x}{10}}dx
integral of-tan^2(x)	\int\:-\tan^{2}(x)dx
integral of x/(sqrt(121x^2-1))	\int\:\frac{x}{\sqrt{121x^{2}-1}}dx
derivative of y=2^{-x}	derivative\:y=2^{-x}
integral of (2w^2-w)e^{7w-1}	\int\:(2w^{2}-w)e^{7w-1}dw
integral of (4-x^2)/(2+x)	\int\:\frac{4-x^{2}}{2+x}dx
(dy)/(dt)=3y	\frac{dy}{dt}=3y
tangent of y=x^{3-5x^2}+7x+3	tangent\:y=x^{3-5x^{2}}+7x+3
integral of (x^2+2x-1)/(x(2x-1)(x+2))	\int\:\frac{x^{2}+2x-1}{x(2x-1)(x+2)}dx
integral of (sin(x))/(sqrt(1-cos^2(x)))	\int\:\frac{\sin(x)}{\sqrt{1-\cos^{2}(x)}}dx
area-3x^2-10x,3	area\:-3x^{2}-10x,3
integral of (3x^2)/x	\int\:\frac{3x^{2}}{x}dx
integral from 0 to 1 of 6/(x^2+2x-8)	\int\:_{0}^{1}\frac{6}{x^{2}+2x-8}dx
integral of (-x-2)/(3(x^2+x+1))	\int\:\frac{-x-2}{3(x^{2}+x+1)}dx
limit as x approaches 0 of ((3+x)-(3))/x	\lim\:_{x\to\:0}(\frac{(3+x)-(3)}{x})
12y^{''}-5y^'-2y=0	12y^{\prime\:\prime\:}-5y^{\prime\:}-2y=0
y^'=7y^2	y^{\prime\:}=7y^{2}
derivative of (sqrt(x)/(\sqrt[3]{2x)})	\frac{d}{dx}(\frac{\sqrt{x}}{\sqrt[3]{2x}})
(\partial)/(\partial y)(8x^{5y})	\frac{\partial\:}{\partial\:y}(8x^{5y})
(dy)/(dt)=2y(1-y/2)	\frac{dy}{dt}=2y(1-\frac{y}{2})
derivative of (2-x/(x+1))	\frac{d}{dx}(\frac{2-x}{x+1})
(dy)/(dx)=x+y+1	\frac{dy}{dx}=x+y+1
derivative of f(x)=(x+1)^3	derivative\:f(x)=(x+1)^{3}
((x^2}{100}+8+\frac{20)/x)^'	(\frac{x^{2}}{100}+8+\frac{20}{x})^{\prime\:}
3y^{''}+6y^'+2y=0	3y^{\prime\:\prime\:}+6y^{\prime\:}+2y=0
integral from 1 to e of (ln(x))/(x^3)	\int\:_{1}^{e}\frac{\ln(x)}{x^{3}}dx
derivative of f(θ)=3tan(θ)	derivative\:f(θ)=3\tan(θ)
limit as x approaches+(-3) of 5	\lim\:_{x\to\:+(-3)}(5)
derivative of ln(sin(x/2))	\frac{d}{dx}(\ln(\sin(\frac{x}{2})))
integral of (3^{5x-2})	\int\:(3^{5x-2})dx
integral from-1 to 3 of 3xe^{2x^2-5}	\int\:_{-1}^{3}3xe^{2x^{2}-5}dx
limit as x approaches 1 of (\sqrt[3]{x+7}-2)/(x^3-1)	\lim\:_{x\to\:1}(\frac{\sqrt[3]{x+7}-2}{x^{3}-1})
integral of sqrt(x)+x	\int\:\sqrt{x}+xdx
limit as x approaches 0 of (x-5)/(x-1)	\lim\:_{x\to\:0}(\frac{x-5}{x-1})
tangent of y=(sqrt(5))^x	tangent\:y=(\sqrt{5})^{x}
(\partial)/(\partial x)(x^2z+y,x+y,y+z^2)	\frac{\partial\:}{\partial\:x}(x^{2}z+y,x+y,y+z^{2})
4x^2(dy)/(dx)=(dy)/(dx)+9xe^{-y}	4x^{2}\frac{dy}{dx}=\frac{dy}{dx}+9xe^{-y}
derivative of x^2-2x+3	derivative\:x^{2}-2x+3
tangent of f(x)=(3x)/(x^2-6),3,\at x=3	tangent\:f(x)=\frac{3x}{x^{2}-6},3,\at\:x=3
derivative of (8sqrt(5))/(15)x^{3/2}-2	derivative\:\frac{8\sqrt{5}}{15}x^{\frac{3}{2}}-2
integral of cos^3(7x)sin^{-2}(7x)	\int\:\cos^{3}(7x)\sin^{-2}(7x)dx
x^'=-x	x^{\prime\:}=-x
integral of (-7x)	\int\:(-7x)dx
integral from-2 to 3 of 5/(x^4)	\int\:_{-2}^{3}\frac{5}{x^{4}}dx
sum from n=1 to infinity of 3	\sum\:_{n=1}^{\infty\:}3
integral of (x-sin(x))	\int\:(x-\sin(x))dx
integral of (x^2+9x)cos(x)	\int\:(x^{2}+9x)\cos(x)dx
limit as x approaches infinity+of (x^3)/(1e^{x/4)}	\lim\:_{x\to\:\infty\:+}(\frac{x^{3}}{1e^{\frac{x}{4}}})
(\partial)/(\partial x)(x^{ey})	\frac{\partial\:}{\partial\:x}(x^{ey})
integral of 1/(x^2+3x+4)	\int\:\frac{1}{x^{2}+3x+4}dx
integral of 1/(81e^{-7x)+e^{7x}}	\int\:\frac{1}{81e^{-7x}+e^{7x}}dx
integral of ((x^2-4))/(x(x^2+4))	\int\:\frac{(x^{2}-4)}{x(x^{2}+4)}dx
(\partial)/(\partial x)(y^2z)	\frac{\partial\:}{\partial\:x}(y^{2}z)
integral from 0.6 to 1.5 of (48+8y)/(81)	\int\:_{0.6}^{1.5}\frac{48+8y}{81}dy
limit as x approaches infinity+of 65.4-65.4e^{(-(7x)/(2180))}	\lim\:_{x\to\:\infty\:+}(65.4-65.4e^{(-\frac{7x}{2180})})
slope ofintercept (-2,-4),(2,5)	slopeintercept\:(-2,-4),(2,5)

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