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Popular Calculus Problems

derivative of sin^5(2x)	\frac{d}{dx}(\sin^{5}(2x))
xy^'-x^2y=-x^2	xy^{\prime\:}-x^{2}y=-x^{2}
(\partial)/(\partial y)(-1/(x^2y))	\frac{\partial\:}{\partial\:y}(-\frac{1}{x^{2}y})
integral of cos(5x+7)	\int\:\cos(5x+7)dx
y^'=3-6x+y-2xy	y^{\prime\:}=3-6x+y-2xy
integral of sin(3x)+cos(5x)	\int\:\sin(3x)+\cos(5x)dx
inverse oflaplace (3s+3)/(s^2-9)	inverselaplace\:\frac{3s+3}{s^{2}-9}
(\partial)/(\partial x)(sqrt(2(x+c)))	\frac{\partial\:}{\partial\:x}(\sqrt{2(x+c)})
integral of 3t^3	\int\:3t^{3}dt
derivative of f(x)=ln(1+x)	derivative\:f(x)=\ln(1+x)
integral of (ax+b)^n	\int\:(ax+b)^{n}dx
derivative of e^{3x}*cos(2x)	\frac{d}{dx}(e^{3x}\cdot\:\cos(2x))
integral from 0 to pi/(12) of 6tan(3x)	\int\:_{0}^{\frac{π}{12}}6\tan(3x)dx
limit as x approaches 2 of 2x^3-3x^2+4x-9	\lim\:_{x\to\:2}(2x^{3}-3x^{2}+4x-9)
y^{''}+2y^'+y=xe^{-x}	y^{\prime\:\prime\:}+2y^{\prime\:}+y=xe^{-x}
limit as x approaches 0 of 3/(x(x+3)^2)	\lim\:_{x\to\:0}(\frac{3}{x(x+3)^{2}})
integral from 1 to e of xln(x)	\int\:_{1}^{e}x\ln(x)dx
(d^2y)/(dx^2)-y=0	\frac{d^{2}y}{dx^{2}}-y=0
limit as x approaches 0 of 3(x)^{x/2}	\lim\:_{x\to\:0}(3(x)^{\frac{x}{2}})
integral of xe^{x+2}	\int\:xe^{x+2}dx
sum from n=1 to infinity of ((x-1)^n)/n	\sum\:_{n=1}^{\infty\:}\frac{(x-1)^{n}}{n}
derivative of \sqrt[6]{t}-6e^t	derivative\:\sqrt[6]{t}-6e^{t}
integral of sin^4(y)cos^7(y)	\int\:\sin^{4}(y)\cos^{7}(y)dy
implicit (d^2y)/(dx^2),x^2+y^2=36	implicit\:\frac{d^{2}y}{dx^{2}},x^{2}+y^{2}=36
derivative of (2d/(x^3)-a)	\frac{d}{dx}(\frac{2d}{x^{3}}-a)
integral of (10)/(sqrt(9-16x^2))	\int\:\frac{10}{\sqrt{9-16x^{2}}}dx
(\partial)/(\partial x)(4/(1+x^2))	\frac{\partial\:}{\partial\:x}(\frac{4}{1+x^{2}})
integral of 7/2 x^2	\int\:\frac{7}{2}x^{2}dx
derivative of 4cos(2x)	derivative\:4\cos(2x)
implicit (dy)/(dx),y=x^{-10cos(x)}	implicit\:\frac{dy}{dx},y=x^{-10\cos(x)}
y^'=(y+5)(x+2)	y^{\prime\:}=(y+5)(x+2)
tangent of f(x)= 7/x ,\at x=4	tangent\:f(x)=\frac{7}{x},\at\:x=4
derivative of (7e^x)/((7+e^x)^2)	derivative\:\frac{7e^{x}}{(7+e^{x})^{2}}
integral of 1/(sqrt(x^2+10))	\int\:\frac{1}{\sqrt{x^{2}+10}}dx
integral of xin^2x	\int\:xin^{2}xdx
integral of sec(x)	\int\:\sec(x)dx
integral of u/(1-u^2)	\int\:\frac{u}{1-u^{2}}du
derivative of 2ln(4x)	\frac{d}{dx}(2\ln(4x))
derivative of (sqrt(x)/3)	\frac{d}{dx}(\frac{\sqrt{x}}{3})
(\partial)/(\partial x)(1/(r^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{r^{2}})
derivative of f(x)=csc^2(x)	derivative\:f(x)=\csc^{2}(x)
integral of 1/(1-x)	\int\:\frac{1}{1-x}dx
derivative of-2csc(x+4cot(x))	\frac{d}{dx}(-2\csc(x)+4\cot(x))
(dP)/(dt)=k*P	\frac{dP}{dt}=k\cdot\:P
(xy-1)dx+(x^2-xy)dy=0	(xy-1)dx+(x^{2}-xy)dy=0
(dy)/(dx)=y(10-y)	\frac{dy}{dx}=y(10-y)
derivative of 8sin(x-8xcos(x))	\frac{d}{dx}(8\sin(x)-8x\cos(x))
derivative of ln(9x)	derivative\:\ln(9x)
derivative of f(x)=2x^3-3x^2-72x+108	derivative\:f(x)=2x^{3}-3x^{2}-72x+108
integral of (csc^2(t)-2e^t)	\int\:(\csc^{2}(t)-2e^{t})dt
derivative of sqrt(ln(-5x+2x^{-2)})	\frac{d}{dx}(\sqrt{\ln(-5x+2x^{-2})})
derivative of xe^{x^2-y}	\frac{d}{dx}(xe^{x^{2}-y})
derivative of (1+sqrt(t))(2t^2-7)	derivative\:(1+\sqrt{t})(2t^{2}-7)
integral of 4/(sqrt(1-x^2))	\int\:\frac{4}{\sqrt{1-x^{2}}}dx
derivative of sin(3ln(x))	derivative\:\sin(3\ln(x))
(\partial)/(\partial x)(3ln(x+y)-3x)	\frac{\partial\:}{\partial\:x}(3\ln(x+y)-3x)
derivative of pit+cos((4pit+pi)/2)	derivative\:πt+\cos(\frac{4πt+π}{2})
derivative of sqrt(2500-x^2)	\frac{d}{dx}(\sqrt{2500-x^{2}})
integral from 0 to 1 of t^2e^{-2t}	\int\:_{0}^{1}t^{2}e^{-2t}dt
integral of (e^x)/((e^x-6)(e^{2x)+1)}	\int\:\frac{e^{x}}{(e^{x}-6)(e^{2x}+1)}dx
derivative of f(x)= x/(x+17)	derivative\:f(x)=\frac{x}{x+17}
integral of 3x-2sqrt(x)	\int\:3x-2\sqrt{x}dx
(\partial)/(\partial y)(ye^{xy})	\frac{\partial\:}{\partial\:y}(ye^{xy})
limit as x approaches 0 of sin(1)	\lim\:_{x\to\:0}(\sin(1))
integral of sqrt(1+(x-1)^{1/2)}	\int\:\sqrt{1+(x-1)^{\frac{1}{2}}}dx
slope of (-1,6),(2,-3)	slope\:(-1,6),(2,-3)
area x+y^2=56,x=y	area\:x+y^{2}=56,x=y
integral of (x^2-1)/(sqrt(2x-1))	\int\:\frac{x^{2}-1}{\sqrt{2x-1}}dx
derivative of (x^3-1/x)	\frac{d}{dx}(\frac{x^{3}-1}{x})
derivative of e^{-15x}	\frac{d}{dx}(e^{-15x})
(\partial)/(\partial x)(48x^3cos(6x^2y))	\frac{\partial\:}{\partial\:x}(48x^{3}\cos(6x^{2}y))
derivative of (x-3/x)	\frac{d}{dx}(\frac{x-3}{x})
integral of csc^2(u)	\int\:\csc^{2}(u)du
integral of sin(1/6 x)	\int\:\sin(\frac{1}{6}x)dx
integral from 1 to 2 of 1/(x^2+3x)	\int\:_{1}^{2}\frac{1}{x^{2}+3x}dx
integral of 6/(x^2-9)	\int\:\frac{6}{x^{2}-9}dx
integral of (x^2)/((81+x^2)^2)	\int\:\frac{x^{2}}{(81+x^{2})^{2}}dx
derivative of 3x^3e^x	\frac{d}{dx}(3x^{3}e^{x})
derivative of x^{7sin(x})	\frac{d}{dx}(x^{7\sin(x)})
d/(du)(u^2+v^2)	\frac{d}{du}(u^{2}+v^{2})
implicit (dy)/(dx),3x^2y^3=3x-2y^2-16	implicit\:\frac{dy}{dx},3x^{2}y^{3}=3x-2y^{2}-16
derivative of (x-3)^{2/3}	derivative\:(x-3)^{\frac{2}{3}}
y^'=(6x)/y	y^{\prime\:}=\frac{6x}{y}
derivative of [x+(x+sin^2(x))^4]^3	derivative\:[x+(x+\sin^{2}(x))^{4}]^{3}
integral of (3x^2+x+4)/(x^4+3x^2+2)	\int\:\frac{3x^{2}+x+4}{x^{4}+3x^{2}+2}dx
derivative of x^4ln(9x)	\frac{d}{dx}(x^{4}\ln(9x))
derivative of 2x^2-5x+1	\frac{d}{dx}(2x^{2}-5x+1)
y^'+3x^{-1}y=x^2	y^{\prime\:}+3x^{-1}y=x^{2}
integral from 1 to 2 of x^4ln(x)	\int\:_{1}^{2}x^{4}\ln(x)dx
derivative of 6x^{-1}	\frac{d}{dx}(6x^{-1})
derivative of e^{(cos(t)+ln(t))}	derivative\:e^{(\cos(t)+\ln(t))}
limit as x approaches infinity of 1/(2x)	\lim\:_{x\to\:\infty\:}(\frac{1}{2x})
derivative of ln(ln(2x^3))	\frac{d}{dx}(\ln(\ln(2x^{3})))
derivative of (sqrt(x)-6)/(sqrt(x)+6)	derivative\:\frac{\sqrt{x}-6}{\sqrt{x}+6}
laplacetransform 7+3t+2t^2-5t^3	laplacetransform\:7+3t+2t^{2}-5t^{3}
derivative of 4/(sqrt(x+7))	\frac{d}{dx}(\frac{4}{\sqrt{x}+7})
tangent of y= 2/((x-2))	tangent\:y=\frac{2}{(x-2)}
integral from 0 to 6 of pi(sqrt(x-1))^2	\int\:_{0}^{6}π(\sqrt{x-1})^{2}dx
x^2y^'+8xy=17y^3	x^{2}y^{\prime\:}+8xy=17y^{3}
integral of (2xarcsin(x))/(sqrt(1-x^2))	\int\:\frac{2x\arcsin(x)}{\sqrt{1-x^{2}}}dx

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