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Popular Calculus Problems

derivative of y=ln(7x^2+3y^2)	derivative\:y=\ln(7x^{2}+3y^{2})
2y^{''}+3y^'+y=t^2+3sin(t)	2y^{\prime\:\prime\:}+3y^{\prime\:}+y=t^{2}+3\sin(t)
integral of ((3*ln(x)-5)^4)/x	\int\:\frac{(3\cdot\:\ln(x)-5)^{4}}{x}dx
y^'=7e^{4x-5y},y(0)=0	y^{\prime\:}=7e^{4x-5y},y(0)=0
inverse oflaplace 2/((s^2+3))	inverselaplace\:\frac{2}{(s^{2}+3)}
integral from-5 to-2 of 3 1/x	\int\:_{-5}^{-2}3\frac{1}{x}dx
integral from 1 to 6 of t^4ln(4t)	\int\:_{1}^{6}t^{4}\ln(4t)dt
derivative of 5pi^2	\frac{d}{dx}(5π^{2})
integral of 9sin(x)	\int\:9\sin(x)dx
derivative of arcsinh(sqrt(3x))	\frac{d}{dx}(\arcsinh(\sqrt{3x}))
integral of xe^{9x}	\int\:xe^{9x}dx
integral of e^{z/y}	\int\:e^{\frac{z}{y}}dz
derivative of 3/(x^{-2})	\frac{d}{dx}(\frac{3}{x^{-2}})
(\partial)/(\partial x)(1+x^2y-sqrt(xy))	\frac{\partial\:}{\partial\:x}(1+x^{2}y-\sqrt{xy})
d/(dt)(2t+2)	\frac{d}{dt}(2t+2)
derivative of 3(x+1^2)	\frac{d}{dx}(3(x+1)^{2})
inverse oflaplace (4s)/(s^2-16)	inverselaplace\:\frac{4s}{s^{2}-16}
derivative of sin(x+pi/2-cos(x))	\frac{d}{dx}(\sin(x+\frac{π}{2})-\cos(x))
derivative of 1-3x^2	derivative\:1-3x^{2}
12x^3-3ysqrt(x^4+1)(dy)/(dx)=0	12x^{3}-3y\sqrt{x^{4}+1}\frac{dy}{dx}=0
integral from 0 to 4 of 2^s	\int\:_{0}^{4}2^{s}ds
y^'+3y=e^{-4t}	y^{\prime\:}+3y=e^{-4t}
integral from 0 to 2 of 4x-x^3	\int\:_{0}^{2}4x-x^{3}dx
derivative of e^t(cos(t))	derivative\:e^{t}(\cos(t))
area x=-2,x=2,y=2x^2+5,y=0	area\:x=-2,x=2,y=2x^{2}+5,y=0
derivative of sin(-1(6x+1))	derivative\:\sin(-1(6x+1))
inverse oflaplace 2/(s(s+2))	inverselaplace\:\frac{2}{s(s+2)}
integral of (cos(x))/((sin(x))^3)	\int\:\frac{\cos(x)}{(\sin(x))^{3}}dx
limit as x approaches-7+of ((-6x))/(x+7)	\lim\:_{x\to\:-7+}(\frac{(-6x)}{x+7})
(d^2)/(dx^2)(ln(x^2+1))	\frac{d^{2}}{dx^{2}}(\ln(x^{2}+1))
y^{''}+6y^'+9y=6cos(t)+8sin(t)	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=6\cos(t)+8\sin(t)
limit as x approaches 0+of (1-8x)^{1/x}	\lim\:_{x\to\:0+}((1-8x)^{\frac{1}{x}})
f(x)=x^2ln(7x)	f(x)=x^{2}\ln(7x)
derivative of e^{xsin(x})	\frac{d}{dx}(e^{x\sin(x)})
integral of (x^2sqrt(x^3+1))	\int\:(x^{2}\sqrt{x^{3}+1})dx
(dy)/(dt)=0.225-0.0045y	\frac{dy}{dt}=0.225-0.0045y
integral of sin^5(8θ)	\int\:\sin^{5}(8θ)dθ
derivative of arcsec(e^x)	\frac{d}{dx}(\arcsec(e^{x}))
slope of (2)(1)	slope\:(2)(1)
integral from 2 to 1 of x^2	\int\:_{2}^{1}x^{2}dx
limit as x approaches 1+of 1/x	\lim\:_{x\to\:1+}(\frac{1}{x})
derivative of e^{5-x}	\frac{d}{dx}(e^{5-x})
derivative of f(x)=22x^{3/2}-8x^{1/2}	derivative\:f(x)=22x^{\frac{3}{2}}-8x^{\frac{1}{2}}
limit as x approaches 0 of+(x+4)	\lim\:_{x\to\:0}(+(x+4))
d/(dy)(y^3sin(6x))	\frac{d}{dy}(y^{3}\sin(6x))
derivative of y= 4/((3x)^3)+2cos(x)	derivative\:y=\frac{4}{(3x)^{3}}+2\cos(x)
integral of (2x-3)/(x^3+10x)	\int\:\frac{2x-3}{x^{3}+10x}dx
derivative of ((x-7/(x+4))^{10})	\frac{d}{dx}((\frac{x-7}{x+4})^{10})
integral of sin(1/6)xsin(1/12)x	\int\:\sin(\frac{1}{6})x\sin(\frac{1}{12})xdx
limit as x approaches 0 of (3e^x)/(x+1)	\lim\:_{x\to\:0}(\frac{3e^{x}}{x+1})
y^'=x^2+4	y^{\prime\:}=x^{2}+4
derivative of x/(1+(1.5574+6.09x^2^2))	\frac{d}{dx}(\frac{x}{1+(1.5574+6.09x^{2})^{2}})
(\partial)/(\partial x)(e^x+ycos(xy))	\frac{\partial\:}{\partial\:x}(e^{x}+y\cos(xy))
integral of (-1/x)	\int\:(-\frac{1}{x})dx
(\partial)/(\partial y)(x^2y+zcos(y))	\frac{\partial\:}{\partial\:y}(x^{2}y+z\cos(y))
derivative of sin(-2ln(1-2x))	\frac{d}{dx}(\sin(-2\ln(1-2x)))
derivative of x/(x^2-3)	derivative\:\frac{x}{x^{2}-3}
y^'+1/x y=4(x+7)^2	y^{\prime\:}+\frac{1}{x}y=4(x+7)^{2}
derivative of 4x(x^2-1)	derivative\:4x(x^{2}-1)
(dy)/(dt)=16-y/(250+0t)	\frac{dy}{dt}=16-\frac{y}{250+0t}
derivative of y=3x^2+10x-26	derivative\:y=3x^{2}+10x-26
integral of sin^5(x)cos(x)	\int\:\sin^{5}(x)\cos(x)dx
derivative of x^{sin(2x})	\frac{d}{dx}(x^{\sin(2x)})
derivative of sin^2(x-cos^2(x)sin^2(x))	\frac{d}{dx}(\sin^{2}(x)-\cos^{2}(x)\sin^{2}(x))
(\partial)/(\partial x)(xy^2)	\frac{\partial\:}{\partial\:x}(xy^{2})
tangent of f(x)=10sqrt(x),(1,10)	tangent\:f(x)=10\sqrt{x},(1,10)
derivative of y=arccos(4x^2)	derivative\:y=\arccos(4x^{2})
area y=x^2,y=x+2	area\:y=x^{2},y=x+2
integral of (9-x^2)^{3/2}	\int\:(9-x^{2})^{\frac{3}{2}}dx
integral of 1/(36x^2+1)	\int\:\frac{1}{36x^{2}+1}dx
(tan(θ))^'	(\tan(θ))^{\prime\:}
area x=y^3,x=y^2	area\:x=y^{3},x=y^{2}
integral of ((x+2))/(x^2+4x+5)	\int\:\frac{(x+2)}{x^{2}+4x+5}dx
derivative of-4xy	\frac{d}{dx}(-4xy)
integral of tan^3(x)sin(x)	\int\:\tan^{3}(x)\sin(x)dx
integral of (2x^3+5)x	\int\:(2x^{3}+5)xdx
limit as x approaches 1 of (x^2-2)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{2}-2}{x-1})
(\partial)/(\partial y)(y/(1+x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{y}{1+x^{2}+y^{2}})
derivative of e^x+x-3/2 e^{2x}+e^{2x}x	\frac{d}{dx}(e^{x}+x-\frac{3}{2}e^{2x}+e^{2x}x)
integral of cot(x/7)	\int\:\cot(\frac{x}{7})dx
derivative of sqrt(2x-4)	\frac{d}{dx}(\sqrt{2x-4})
derivative of 2^{2^n}	derivative\:2^{2^{n}}
integral of 1/(x^2sqrt(a^2+x^2))	\int\:\frac{1}{x^{2}\sqrt{a^{2}+x^{2}}}dx
inverse oflaplace e^{-t}	inverselaplace\:e^{-t}
derivative of cx^{-4}	\frac{d}{dx}(cx^{-4})
integral of (2x^2+9)(x-3)^8	\int\:(2x^{2}+9)(x-3)^{8}dx
(\partial)/(\partial x)(x^2-y^2)	\frac{\partial\:}{\partial\:x}(x^{2}-y^{2})
(\partial)/(\partial y)(ln(1+x^2+y^2))	\frac{\partial\:}{\partial\:y}(\ln(1+x^{2}+y^{2}))
derivative of-sec(7x)-ln(6x)	derivative\:-\sec(7x)-\ln(6x)
xy^'-y=x^{2017}y^2	xy^{\prime\:}-y=x^{2017}y^{2}
laplacetransform e^{3t}t^2	laplacetransform\:e^{3t}t^{2}
integral of c^3t	\int\:c^{3}tdt
slope of (-2,-1),(3,4)	slope\:(-2,-1),(3,4)
integral of (x-4)/(sqrt(x^2-8x+1))	\int\:\frac{x-4}{\sqrt{x^{2}-8x+1}}dx
limit as t approaches 3-of (t^2)/(9-t^2)	\lim\:_{t\to\:3-}(\frac{t^{2}}{9-t^{2}})
integral of (x^2)/(x^2+8)	\int\:\frac{x^{2}}{x^{2}+8}dx
derivative of (e^x-1)/(x^2+1)	derivative\:\frac{e^{x}-1}{x^{2}+1}
y^{''}-4y^'+4=0	y^{\prime\:\prime\:}-4y^{\prime\:}+4=0
sum from n=0 to infinity of ((3^n))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(3^{n})}{n!}
(\partial)/(\partial x)(xy^2-e^{xy})	\frac{\partial\:}{\partial\:x}(xy^{2}-e^{xy})

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