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Popular Calculus Problems

derivative of 20	\frac{d}{dx}(20)
integral from-2 to 2 of 1/((x+4)(x-4))	\int\:_{-2}^{2}\frac{1}{(x+4)(x-4)}dx
sum from i=0 to infinity of 2^i	\sum\:_{i=0}^{\infty\:}2^{i}
y^'=(y^2)/(x^2)+y/x	y^{\prime\:}=\frac{y^{2}}{x^{2}}+\frac{y}{x}
derivative of (sqrt(x^2+4))/3+(11-x)/4	derivative\:\frac{\sqrt{x^{2}+4}}{3}+\frac{11-x}{4}
integral from 0 to 2 of 5x^2	\int\:_{0}^{2}5x^{2}dx
derivative of 6sin(3x)	derivative\:6\sin(3x)
integral of (x^4-3)^2	\int\:(x^{4}-3)^{2}dx
d/(dt)(-2sin(2t))	\frac{d}{dt}(-2\sin(2t))
limit as x approaches 4 of 4x	\lim\:_{x\to\:4}(4x)
integral of (ln(x))/(xsqrt(x))	\int\:\frac{\ln(x)}{x\sqrt{x}}dx
sum from n=1 to infinity of 1/((n(n+2)))	\sum\:_{n=1}^{\infty\:}\frac{1}{(n(n+2))}
integral of (1/(x^{-0.1)})	\int\:(\frac{1}{x^{-0.1}})dx
y^'=(x+y-1)^2	y^{\prime\:}=(x+y-1)^{2}
(\partial)/(\partial x)(2xy+5y^2)	\frac{\partial\:}{\partial\:x}(2xy+5y^{2})
derivative of (arctan(9x))^2	derivative\:(\arctan(9x))^{2}
derivative of (e^x)/(5x-2)	derivative\:\frac{e^{x}}{5x-2}
integral from 0 to 2pi of sin^2(9x)	\int\:_{0}^{2π}\sin^{2}(9x)dx
laplacetransform 4t	laplacetransform\:4t
limit as x approaches 0 of ln(1+sin(x))	\lim\:_{x\to\:0}(\ln(1+\sin(x)))
(dy)/(dx)=x^7y	\frac{dy}{dx}=x^{7}y
derivative of ln(sinh(x))	\frac{d}{dx}(\ln(\sinh(x)))
integral of cos((npix)/2)	\int\:\cos(\frac{nπx}{2})dx
integral of ((sqrt(100-x^2)))/x	\int\:\frac{(\sqrt{100-x^{2}})}{x}dx
limit as x approaches infinity of 7e^x	\lim\:_{x\to\:\infty\:}(7e^{x})
maclaurin (1-x)^{-1/2}	maclaurin\:(1-x)^{-\frac{1}{2}}
f(x)=x^2e^{2x}	f(x)=x^{2}e^{2x}
(cos(2x))^'	(\cos(2x))^{\prime\:}
derivative of 2*x	\frac{d}{dx}(2\cdot\:x)
derivative of sqrt(x)+2x	\frac{d}{dx}(\sqrt{x}+2x)
derivative of 6e^{3x}	\frac{d}{dx}(6e^{3x})
integral of (a^2-x^{2/3})	\int\:(a^{2}-x^{\frac{2}{3}})dx
limit as x approaches 0+of ln(1+sin(x))	\lim\:_{x\to\:0+}(\ln(1+\sin(x)))
derivative of e^{sin^2(x)}	derivative\:e^{\sin^{2}(x)}
integral of x^3sin(2x)	\int\:x^{3}\sin(2x)dx
derivative of-3sin(2x-6cos(x))	\frac{d}{dx}(-3\sin(2x)-6\cos(x))
derivative of sin(25x^2+6x+4)	\frac{d}{dx}(\sin(25x^{2}+6x+4))
derivative of (8x/(x^2+4))	\frac{d}{dx}(\frac{8x}{x^{2}+4})
(dy)/(dx)=(1+2y^2)/(y*sin(x))	\frac{dy}{dx}=\frac{1+2y^{2}}{y\cdot\:\sin(x)}
derivative of ({f}(x)/({g)(x)+1})	\frac{d}{dx}(\frac{{f}(x)}{{g}(x)+1})
tangent of-2sin(x),\at x= 3/4 pi	tangent\:-2\sin(x),\at\:x=\frac{3}{4}π
derivative of acos(3x+bsin(3x))	\frac{d}{dx}(a\cos(3x)+b\sin(3x))
integral of (3t^2-4t-4)	\int\:(3t^{2}-4t-4)dt
derivative of sin^3(x^3-2x)	derivative\:\sin^{3}(x^{3}-2x)
integral from 0 to 3 of te^{-t}	\int\:_{0}^{3}te^{-t}dt
integral of 6x^2-5x+3	\int\:6x^{2}-5x+3dx
integral of (6sin(2x)-4cos(4x))	\int\:(6\sin(2x)-4\cos(4x))dx
area y^2=4x,4x-3y=4	area\:y^{2}=4x,4x-3y=4
derivative of (arctan(9x))^2	derivative\:(\arctan(9x))^{2}
derivative of 1/(x^5)	derivative\:\frac{1}{x^{5}}
derivative of 9e^{-x}-3e^{-4x}	derivative\:9e^{-x}-3e^{-4x}
integral of sec(t)(5sec(t)+2tan(t))	\int\:\sec(t)(5\sec(t)+2\tan(t))dt
integral from 1 to 5 of x/(sqrt(2x-1))	\int\:_{1}^{5}\frac{x}{\sqrt{2x-1}}dx
limit as x approaches 0 of cos(x)+sin(x)	\lim\:_{x\to\:0}(\cos(x)+\sin(x))
tangent of (x+2)^2+(y-3)^2=37,(4,2)	tangent\:(x+2)^{2}+(y-3)^{2}=37,(4,2)
(dy)/(dx)=((y^2-1))/(x^2-1),y(7)=7	\frac{dy}{dx}=\frac{(y^{2}-1)}{x^{2}-1},y(7)=7
integral of e^{x/5}	\int\:e^{\frac{x}{5}}dx
y^'=8x^3+2 y/x	y^{\prime\:}=8x^{3}+2\frac{y}{x}
(dy)/(dt)=-2y,y(0)=2	\frac{dy}{dt}=-2y,y(0)=2
integral of 1/((4+x^2)^3)	\int\:\frac{1}{(4+x^{2})^{3}}dx
sum from n=1 to infinity of n(5/4)^n	\sum\:_{n=1}^{\infty\:}n(\frac{5}{4})^{n}
(\partial)/(\partial x)(x^3y^5)	\frac{\partial\:}{\partial\:x}(x^{3}y^{5})
derivative of \sqrt[3]{x^2+3x-4}	\frac{d}{dx}(\sqrt[3]{x^{2}+3x-4})
integral of (sin(x))/(1+x^2)	\int\:\frac{\sin(x)}{1+x^{2}}dx
derivative of (x^{12})^5	derivative\:(x^{12})^{5}
derivative of 1/2 x-1/4	\frac{d}{dx}(\frac{1}{2}x-\frac{1}{4})
(\partial)/(\partial x)(3xye^{-x^2y})	\frac{\partial\:}{\partial\:x}(3xye^{-x^{2}y})
sum from n=2 to infinity of 1/(n-1)-1/n	\sum\:_{n=2}^{\infty\:}\frac{1}{n-1}-\frac{1}{n}
derivative of sqrt((x^2/4+17))	\frac{d}{dx}(\sqrt{\frac{x^{2}}{4}+17})
limit as n approaches infinity of-1+1/n	\lim\:_{n\to\:\infty\:}(-1+\frac{1}{n})
integral of (x^2+3x-1)/(x^3+8)	\int\:\frac{x^{2}+3x-1}{x^{3}+8}dx
integral of x\sqrt[6]{1+x^2}	\int\:x\sqrt[6]{1+x^{2}}dx
integral of (cos(pi/2))/(x^2)	\int\:\frac{\cos(\frac{π}{2})}{x^{2}}dx
derivative of x^2(1+y^3)	\frac{d}{dx}(x^{2}(1+y)^{3})
derivative of cos^{ln(7x}(x))	\frac{d}{dx}(\cos^{\ln(7x)}(x))
integral of ((2x+sqrt(x)))/(x^3)	\int\:\frac{(2x+\sqrt{x})}{x^{3}}dx
integral of (x)^2	\int\:(x)^{2}dx
derivative of y=4-e^x	derivative\:y=4-e^{x}
integral of 1/x (x+1)^2	\int\:\frac{1}{x}(x+1)^{2}dx
limit as x approaches 0 of xe^{-2/(x^2)}	\lim\:_{x\to\:0}(xe^{-\frac{2}{x^{2}}})
integral of (x^4)/(x^5+1)	\int\:\frac{x^{4}}{x^{5}+1}dx
(dy)/(dx)=(cos(19x))/(e^{19y)}	\frac{dy}{dx}=\frac{\cos(19x)}{e^{19y}}
derivative of xcos(x-picos(x)+2sin(x))	\frac{d}{dx}(x\cos(x)-π\cos(x)+2\sin(x))
6y^{''}+y^'-y=0	6y^{\prime\:\prime\:}+y^{\prime\:}-y=0
derivative of 144-x^2	derivative\:144-x^{2}
integral from 0 to pi/3 of cos^3(x)	\int\:_{0}^{\frac{π}{3}}\cos^{3}(x)dx
derivative of sqrt(2-e^x)	\frac{d}{dx}(\sqrt{2-e^{x}})
integral of sin^4(4x)cos^3(4x)	\int\:\sin^{4}(4x)\cos^{3}(4x)dx
integral of 7te^t	\int\:7te^{t}dt
((2+x)dy)/(dx)=3y	\frac{(2+x)dy}{dx}=3y
limit as x approaches a of x	\lim\:_{x\to\:a}(x)
limit as x approaches 7 of sqrt(8x-3)	\lim\:_{x\to\:7}(\sqrt{8x-3})
(\partial)/(\partial u)(tan(uv^3))	\frac{\partial\:}{\partial\:u}(\tan(uv^{3}))
(xy^2+x^3)dx+(y^3+x^2y)dy=0	(xy^{2}+x^{3})dx+(y^{3}+x^{2}y)dy=0
derivative of tan(cos(x))	\frac{d}{dx}(\tan(\cos(x)))
implicit (dy)/(dx),y=x	implicit\:\frac{dy}{dx},y=x
integral of 1/(x^2+2x)	\int\:\frac{1}{x^{2}+2x}dx
integral of (4-3sin(2x))^4cos(2x)	\int\:(4-3\sin(2x))^{4}\cos(2x)dx
derivative of h(a)=2x-5	derivative\:h(a)=2x-5
inverse oflaplace ln((s+5)/(s^2+2s+6))	inverselaplace\:\ln(\frac{s+5}{s^{2}+2s+6})

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