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Popular Calculus Problems

(\partial)/(\partial x)(5ycos(6x))	\frac{\partial\:}{\partial\:x}(5y\cos(6x))
integral of x^2ln(x^2+1)	\int\:x^{2}\ln(x^{2}+1)dx
derivative of e^{-x}x^2+3e^{-x}-e^{-x}	derivative\:e^{-x}x^{2}+3e^{-x}-e^{-x}
xy^'+y+x=0,y(1)=1	xy^{\prime\:}+y+x=0,y(1)=1
(\partial)/(\partial x)(ln(x^5-y^4))	\frac{\partial\:}{\partial\:x}(\ln(x^{5}-y^{4}))
derivative of acos(3x)	\frac{d}{dx}(a\cos(3x))
simplify (3x^2)^{2x}	simplify\:(3x^{2})^{2x}
integral of 1/4 x^{-3/4}	\int\:\frac{1}{4}x^{-\frac{3}{4}}dx
integral of (e^x-e^{-x})	\int\:(e^{x}-e^{-x})dx
(\partial)/(\partial u)(ucos(v))	\frac{\partial\:}{\partial\:u}(u\cos(v))
integral of ((1+cos(3t))/2)	\int\:(\frac{1+\cos(3t)}{2})dt
derivative of x/(sin(2x))	\frac{d}{dx}(\frac{x}{\sin(2x)})
integral of 3x^2-18x+27	\int\:3x^{2}-18x+27dx
derivative of 1/(sqrt(x^7))	\frac{d}{dx}(\frac{1}{\sqrt{x^{7}}})
inverse oflaplace (4s)/(s^2+8s+20)	inverselaplace\:\frac{4s}{s^{2}+8s+20}
derivative of (3x^2-6x-sin(x)^4)	\frac{d}{dx}((3x^{2}-6x-\sin(x))^{4})
integral from x to 2 of 1	\int\:_{x}^{2}1dx
integral of sin(2/x)	\int\:\sin(\frac{2}{x})dx
integral from 0 to 3 of (6x-x^2)	\int\:_{0}^{3}(6x-x^{2})dx
(\partial)/(\partial x)(xy+3x)	\frac{\partial\:}{\partial\:x}(xy+3x)
(1+4x^2)y^'=1	(1+4x^{2})y^{\prime\:}=1
derivative of e^{-kx}	derivative\:e^{-kx}
derivative of arccot(2y)	derivative\:\arccot(2y)
integral from 0 to pi of 9cos^2(x)	\int\:_{0}^{π}9\cos^{2}(x)dx
d/(dy)(-sin(y))	\frac{d}{dy}(-\sin(y))
derivative of 3(7^x)	\frac{d}{dx}(3(7^{x}))
integral of sec^2(3x)tan^2(3x)	\int\:\sec^{2}(3x)\tan^{2}(3x)dx
derivative of ((e^x(2x+3)))/(x^2+1)	derivative\:\frac{(e^{x}(2x+3))}{x^{2}+1}
derivative of (1/(1-x)^2)	\frac{d}{dx}((\frac{1}{1-x})^{2})
tangent of 8/x	tangent\:\frac{8}{x}
(dx)/(dt)+5x=50	\frac{dx}{dt}+5x=50
derivative of (7e^x/(2e^x+1))	\frac{d}{dx}(\frac{7e^{x}}{2e^{x}+1})
integral of (e^x)/(e^{2x)-2e^x-3}	\int\:\frac{e^{x}}{e^{2x}-2e^{x}-3}dx
derivative of (x^3-x)/(1+x^2)	derivative\:\frac{x^{3}-x}{1+x^{2}}
tangent of f(x)=x^2-x,(-4,20)	tangent\:f(x)=x^{2}-x,(-4,20)
xy(dy)/(dx)-y^2=2*x^2	x\cdot\:y\cdot\:\frac{dy}{dx}-y^{2}=2\cdot\:x^{2}
sum from n=4 to infinity of 1/(n(n+1))	\sum\:_{n=4}^{\infty\:}\frac{1}{n(n+1)}
(dy)/(dx)+2/x y=(sin(x))/(x^2)	\frac{dy}{dx}+\frac{2}{x}y=\frac{\sin(x)}{x^{2}}
integral from 0 to 2 of 1/(x+3)	\int\:_{0}^{2}\frac{1}{x+3}dx
derivative of cos(2y)	derivative\:\cos(2y)
integral of 1/(sqrt(y^2-1))	\int\:\frac{1}{\sqrt{y^{2}-1}}dy
sum from n=2 to infinity of 1/(n(n+2))	\sum\:_{n=2}^{\infty\:}\frac{1}{n(n+2)}
xy^'+2y=9x	xy^{\prime\:}+2y=9x
sum from n=1 to infinity}((4)^{n-1 of)/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{(4)^{n-1}}{5^{n}}
taylor 4ln(7+2x^2)	taylor\:4\ln(7+2x^{2})
f(x)= 1/(x^6)	f(x)=\frac{1}{x^{6}}
derivative of sec(x)-6cos(x)	derivative\:\sec(x)-6\cos(x)
(\partial)/(\partial y)(x^y-xy)	\frac{\partial\:}{\partial\:y}(x^{y}-xy)
(dy)/(dx)=2xe^y	\frac{dy}{dx}=2xe^{y}
derivative of (3x^{3x})	\frac{d}{dx}((3x)^{3x})
integral of 1/(a+bx)	\int\:\frac{1}{a+bx}dx
derivative of-4cot(2xcsc(2x))	\frac{d}{dx}(-4\cot(2x)\csc(2x))
y^{''}+2y^'+5y=4sin(2t)	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=4\sin(2t)
derivative of 1/3 cos((6pix-1/2))	\frac{d}{dx}(\frac{1}{3}\cos(\frac{6πx-1}{2}))
integral of x^7sin(x^8)	\int\:x^{7}\sin(x^{8})dx
derivative of e^{x^2}+1	\frac{d}{dx}(e^{x^{2}}+1)
tangent of y=2x^2	tangent\:y=2x^{2}
integral from 0 to y+z of 1/((x+y+z)^3)	\int\:_{0}^{y+z}\frac{1}{(x+y+z)^{3}}dx
derivative of e^x(x-1)	derivative\:e^{x}(x-1)
y^'+sin(t)y=sin(t),y(0)=6	y^{\prime\:}+\sin(t)y=\sin(t),y(0)=6
(\partial)/(\partial x)((x^2-2x)cos(y))	\frac{\partial\:}{\partial\:x}((x^{2}-2x)\cos(y))
derivative of (e^{3x}(cos(2x)))	\frac{d}{dx}((e^{3x})(\cos(2x)))
16y''+8y'+y=0	16y\prime\:\prime\:+8y\prime\:+y=0
limit as x approaches 0 of (tan(4x)cos(6x)-tan(4x))/(24x^3)	\lim\:_{x\to\:0}(\frac{\tan(4x)\cos(6x)-\tan(4x)}{24x^{3}})
limit as x approaches+1 of (x-1)/(x^6-1)	\lim\:_{x\to\:+1}(\frac{x-1}{x^{6}-1})
limit as x approaches 0 of (3x)/(sin(10x))	\lim\:_{x\to\:0}(\frac{3x}{\sin(10x)})
(\partial)/(\partial x)(3(y-1)^3(x-6))	\frac{\partial\:}{\partial\:x}(3(y-1)^{3}(x-6))
integral of (x^3)/(x^2+4x+4)	\int\:\frac{x^{3}}{x^{2}+4x+4}dx
integral of (x-1)^2-4	\int\:(x-1)^{2}-4dx
integral of (x+1)(x+2)	\int\:(x+1)(x+2)dx
limit as x approaches 1 of 1/(x+1)	\lim\:_{x\to\:1}(\frac{1}{x+1})
area f(x)=x^2,x=0,x=2	area\:f(x)=x^{2},x=0,x=2
derivative of (6e^ss-5e^s)/((6s+1)^2)	derivative\:\frac{6e^{s}s-5e^{s}}{(6s+1)^{2}}
integral of (x^3+22)/(x^2+7x+12)	\int\:\frac{x^{3}+22}{x^{2}+7x+12}dx
tangent of y=3e^x+x,(0,3)	tangent\:y=3e^{x}+x,(0,3)
derivative of 2x^2-8	\frac{d}{dx}(2x^{2}-8)
derivative of 7/((7-x^8)^{3/2)}	derivative\:\frac{7}{(7-x^{8})^{\frac{3}{2}}}
derivative of (sin^2(x)+1)^5	derivative\:(\sin^{2}(x)+1)^{5}
derivative of 2t-sin(2t)	derivative\:2t-\sin(2t)
integral of cos^3(x)	\int\:\cos^{3}(x)dx
integral of (x^3+3x)e^{-6x}	\int\:(x^{3}+3x)e^{-6x}dx
(\partial)/(\partial y)(xe^{x^2-y^2})	\frac{\partial\:}{\partial\:y}(xe^{x^{2}-y^{2}})
integral of (4x+3)^9	\int\:(4x+3)^{9}dx
derivative of y=1n(1n(x^3))	derivative\:y=1n(1n(x^{3}))
integral of 7sin^4(x)	\int\:7\sin^{4}(x)dx
derivative of ln(xcos(t))	\frac{d}{dx}(\ln(x)\cos(t))
derivative of cot(e^{2x})	\frac{d}{dx}(\cot(e^{2x}))
y^{''}-6y^'=0	y^{\prime\:\prime\:}-6y^{\prime\:}=0
limit as x approaches 2 of 3x^3-7x^2+3	\lim\:_{x\to\:2}(3x^{3}-7x^{2}+3)
-9x^2y+(dy)/(dx)=-2x^2	-9x^{2}y+\frac{dy}{dx}=-2x^{2}
tangent of ((2x+1))/(x-4)	tangent\:\frac{(2x+1)}{x-4}
derivative of cos^3(1-5x^2)	\frac{d}{dx}(\cos^{3}(1-5x^{2}))
derivative of y=arcsin(5x)	derivative\:y=\arcsin(5x)
derivative of (6x)/(1-cot(x))	derivative\:\frac{6x}{1-\cot(x)}
integral of ((x+1)^3)/((x)^{10)}	\int\:\frac{(x+1)^{3}}{(x)^{10}}dx
derivative of x/(99)	derivative\:\frac{x}{99}
d/(dX)(7.1X+20.3)	\frac{d}{dX}(7.1X+20.3)
derivative of (3x^2-3x+1x^3)	\frac{d}{dx}((3x^{2}-3x+1)x^{3})
integral from 0 to 3 of (3-x)sqrt(x)	\int\:_{0}^{3}(3-x)\sqrt{x}dx
d/(d{y)}({x}(y){z}(y))	\frac{d}{d{y}}({x}(y){z}(y))

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