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Popular Calculus Problems

derivative of (10/(x^7))	\frac{d}{dx}(\frac{10}{x^{7}})
area y=9x,y= 1/3 x,y=10-x^2	area\:y=9x,y=\frac{1}{3}x,y=10-x^{2}
simplify tan(xy)	simplify\:\tan(xy)
derivative of 1-8u^2	derivative\:1-8u^{2}
integral from 0 to 1 of 2pix(e^{-x^2})	\int\:_{0}^{1}2πx(e^{-x^{2}})dx
(\partial)/(\partial x)(-xe^{-2xy})	\frac{\partial\:}{\partial\:x}(-xe^{-2xy})
(d^2)/(dx^2)(θcos(θ))	\frac{d^{2}}{dx^{2}}(θ\cos(θ))
limit as x approaches 0 of 1-(x^2)/4	\lim\:_{x\to\:0}(1-\frac{x^{2}}{4})
limit as x approaches 4 of sqrt(16-x^2)	\lim\:_{x\to\:4}(\sqrt{16-x^{2}})
tangent of g(x)=(3x)/(x-2),(4,6)	tangent\:g(x)=\frac{3x}{x-2},(4,6)
derivative of y=8sqrt(x)	derivative\:y=8\sqrt{x}
taylor sin(x^4)	taylor\:\sin(x^{4})
area y=6x,y=8x^2	area\:y=6x,y=8x^{2}
derivative of sqrt((x+1/(x-5)))	\frac{d}{dx}(\sqrt{\frac{x+1}{x-5}})
derivative of 3ln(2)	derivative\:3\ln(2)
limit as x approaches+7+of 3/(x-7)	\lim\:_{x\to\:+7+}(\frac{3}{x-7})
derivative of y=x^{2/3}	derivative\:y=x^{\frac{2}{3}}
derivative of (x^3-5x(x+2))	\frac{d}{dx}((x^{3}-5x)(x+2))
integral of (x^{1/3})/(x^{4/3)+4}	\int\:\frac{x^{\frac{1}{3}}}{x^{\frac{4}{3}}+4}dx
(dy)/(dx)+4y= 4/3	\frac{dy}{dx}+4y=\frac{4}{3}
(\partial)/(\partial x)(2xe^y-xcos(xy)+2y)	\frac{\partial\:}{\partial\:x}(2xe^{y}-x\cos(xy)+2y)
y^{''}+4sqrt(5)y^'+20y=0	y^{\prime\:\prime\:}+4\sqrt{5}y^{\prime\:}+20y=0
integral of xsqrt(x^4-1)	\int\:x\sqrt{x^{4}-1}dx
derivative of (8x^3-2x^2+3/(2x))	\frac{d}{dx}(\frac{8x^{3}-2x^{2}+3}{2x})
integral of (y-x^3)	\int\:(y-x^{3})dx
integral of (5x-4)/(sqrt(8x-5^2+9))	\int\:\frac{5x-4}{\sqrt{8x-5^{2}+9}}dx
(dy)/(dx)+y^9x+4y=0	\frac{dy}{dx}+y^{9}x+4y=0
integral from 0 to 2 of sqrt(4x+1)	\int\:_{0}^{2}\sqrt{4x+1}dx
limit as x approaches 0 of (ln(6x+1))/x	\lim\:_{x\to\:0}(\frac{\ln(6x+1)}{x})
integral of r/(sqrt(4-r^2))	\int\:\frac{r}{\sqrt{4-r^{2}}}dr
integral of (5x-1)^3	\int\:(5x-1)^{3}dx
tangent of (3x^2)/((3-2x)^4)	tangent\:\frac{3x^{2}}{(3-2x)^{4}}
y^{''}+16y=2sin(2t),y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+16y=2\sin(2t),y(0)=1,y^{\prime\:}(0)=0
integral of (2te^t)	\int\:(2te^{t})dt
tangent of y^4-4y^2=x^4-9x^2,(-3,2)	tangent\:y^{4}-4y^{2}=x^{4}-9x^{2},(-3,2)
derivative of y=e^{4x}cos(7x)	derivative\:y=e^{4x}\cos(7x)
derivative of 4sqrt(x)ln(x)	derivative\:4\sqrt{x}\ln(x)
(\partial)/(\partial y)(5x^2-3xy^2+xyz)	\frac{\partial\:}{\partial\:y}(5x^{2}-3xy^{2}+xyz)
limit as n approaches infinity of 2n	\lim\:_{n\to\:\infty\:}(2n)
limit as x approaches infinity of (2x^2)/(-x+2)	\lim\:_{x\to\:\infty\:}(\frac{2x^{2}}{-x+2})
maclaurin x/(1+4x^2),6	maclaurin\:\frac{x}{1+4x^{2}},6
(\partial)/(\partial x)(inxy)	\frac{\partial\:}{\partial\:x}(inxy)
integral of (y^2)/(16)	\int\:\frac{y^{2}}{16}dy
y^{''}-y=0	y^{\prime\:\prime\:}-y=0
sum from n=0 to infinity of (n!)/(108^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{108^{n}}
integral of (sec^2(5x))/(tan(5x)-4)	\int\:\frac{\sec^{2}(5x)}{\tan(5x)-4}dx
y^'=4y+a	y^{\prime\:}=4y+a
tangent of f(x)=2sqrt(x)-x	tangent\:f(x)=2\sqrt{x}-x
integral from 0 to 2-2x of 1+3x+y	\int\:_{0}^{2-2x}1+3x+ydy
integral of (5x^2+1)(5x^3+3x-8)^6	\int\:(5x^{2}+1)(5x^{3}+3x-8)^{6}dx
(\partial)/(\partial x)(3x^2-2xy+y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}-2xy+y^{2})
derivative of 4sqrt(y^2+7x^2)	derivative\:4\sqrt{y^{2}+7x^{2}}
(\partial)/(\partial x)(2xy^6+x^4y^8)	\frac{\partial\:}{\partial\:x}(2xy^{6}+x^{4}y^{8})
tangent of f(x)=x^2-1/x ,\at x=1	tangent\:f(x)=x^{2}-\frac{1}{x},\at\:x=1
integral of 8sin^5(x)cos(x)	\int\:8\sin^{5}(x)\cos(x)dx
derivative of f(x)=\sqrt[3]{10x^4+11x^3}	derivative\:f(x)=\sqrt[3]{10x^{4}+11x^{3}}
maclaurin (2-3x)cos(3x)	maclaurin\:(2-3x)\cos(3x)
laplacetransform f(t)=(2t-1)^3	laplacetransform\:f(t)=(2t-1)^{3}
2y^'=y^2	2y^{\prime\:}=y^{2}
(\partial)/(\partial x)(y(-sin(xln(y)))ln(y))	\frac{\partial\:}{\partial\:x}(y(-\sin(x\ln(y)))\ln(y))
d/(dt)(-1/(t^2))	\frac{d}{dt}(-\frac{1}{t^{2}})
limit as x approaches 2 of 4-x^2	\lim\:_{x\to\:2}(4-x^{2})
derivative of (Ax^2+Bx+Ce^x)	\frac{d}{dx}((Ax^{2}+Bx+C)e^{x})
derivative of 3sqrt(x-4)	\frac{d}{dx}(3\sqrt{x-4})
limit as x approaches infinity of (e^{3x-8})/(5x)	\lim\:_{x\to\:\infty\:}(\frac{e^{3x-8}}{5x})
integral of (-x+3)	\int\:(-x+3)dx
(\partial)/(\partial x)(arctan(z/x))	\frac{\partial\:}{\partial\:x}(\arctan(\frac{z}{x}))
y^{''}-10y^'+50y=0,y(0)=5,y^'(0)=-2	y^{\prime\:\prime\:}-10y^{\prime\:}+50y=0,y(0)=5,y^{\prime\:}(0)=-2
5y^{''}+30y=0,y(0)=5,y^'(0)=5	5y^{\prime\:\prime\:}+30y=0,y(0)=5,y^{\prime\:}(0)=5
integral of 1/(a^2+u^2)	\int\:\frac{1}{a^{2}+u^{2}}du
(\partial)/(\partial y)((2x-5y)^2)	\frac{\partial\:}{\partial\:y}((2x-5y)^{2})
(10y^2-xy)dx+(x^2)dy=0	(10y^{2}-xy)dx+(x^{2})dy=0
integral of 2x(x^2+3)^2	\int\:2x(x^{2}+3)^{2}dx
24y^{''}+12y^'=0,y(3)=-3,y^'(-4)=4	24y^{\prime\:\prime\:}+12y^{\prime\:}=0,y(3)=-3,y^{\prime\:}(-4)=4
derivative of (2x+9)^2	derivative\:(2x+9)^{2}
integral of (tan(x))/(1-sin^2(x))	\int\:\frac{\tan(x)}{1-\sin^{2}(x)}dx
derivative of f(x)=log_{e}(10x)	derivative\:f(x)=\log_{e}(10x)
(dy)/(dx)=sin^2(y)	\frac{dy}{dx}=\sin^{2}(y)
derivative of arcsec(1/(2x^2-1))	\frac{d}{dx}(\arcsec(\frac{1}{2x^{2}-1}))
integral of (x^2+1)/(x^3-6x^2+12x-8)	\int\:\frac{x^{2}+1}{x^{3}-6x^{2}+12x-8}dx
integral of (u^3)/(u+1)	\int\:\frac{u^{3}}{u+1}du
y^'+3y=2sin(3t)	y^{\prime\:}+3y=2\sin(3t)
derivative of (x^2-35)/(x-6)	derivative\:\frac{x^{2}-35}{x-6}
derivative of-16sin(2x)	derivative\:-16\sin(2x)
integral of sec(1-x)tan(1-x)	\int\:\sec(1-x)\tan(1-x)dx
integral of (-4/(x^3)-8/(x^5))	\int\:(-\frac{4}{x^{3}}-\frac{8}{x^{5}})dx
integral of (sqrt(x))/(x+x^{4/5)}	\int\:\frac{\sqrt{x}}{x+x^{\frac{4}{5}}}dx
integral from 3 to 6 of 8	\int\:_{3}^{6}8dx
integral of-5pisin(pix)	\int\:-5π\sin(πx)dx
integral of 1/((1+x)^3)	\int\:\frac{1}{(1+x)^{3}}dx
derivative of-2/(x^3)	derivative\:-\frac{2}{x^{3}}
derivative of x/(sqrt(x-9))	\frac{d}{dx}(\frac{x}{\sqrt{x-9}})
integral of ((8x-3))/(sqrt(12x-4x^2-5))	\int\:\frac{(8x-3)}{\sqrt{12x-4x^{2}-5}}dx
slope of y=-2-7x^2	slope\:y=-2-7x^{2}
derivative of ((sqrt(x)-6)/(sqrt(x)+6))	\frac{d}{dx}(\frac{(\sqrt{x}-6)}{\sqrt{x}+6})
simplify ((1+sin(t))/(1-cos(t)))^2	simplify\:(\frac{1+\sin(t)}{1-\cos(t)})^{2}
integral from 0 to infinity of 9sin^2(x)	\int\:_{0}^{\infty\:}9\sin^{2}(x)dx
(x-y^2x)dx+(y-x^2y)dy=0	(x-y^{2}x)dx+(y-x^{2}y)dy=0
area x=6-y^2,x=y	area\:x=6-y^{2},x=y
derivative of y=x^3-3x+2	derivative\:y=x^{3}-3x+2

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