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Popular Calculus Problems

limit as x approaches-3+of x/(x^2-9)	\lim\:_{x\to\:-3+}(\frac{x}{x^{2}-9})
limit as x approaches 2 of (x^3-8)/(2x)	\lim\:_{x\to\:2}(\frac{x^{3}-8}{2x})
(\partial)/(\partial x)(xe^{xy}-2y+1)	\frac{\partial\:}{\partial\:x}(xe^{xy}-2y+1)
limit as x approaches 3 of cos(1/(x-3))	\lim\:_{x\to\:3}(\cos(\frac{1}{x-3}))
derivative of e^{sqrt(x^2+y^2)}	\frac{d}{dx}(e^{\sqrt{x^{2}+y^{2}}})
derivative of 0.005x^2-ln(x^{16}+70)	\frac{d}{dx}(0.005x^{2}-\ln(x^{16})+70)
derivative of y=(6x^2+8x+2)/(sqrt(x))	derivative\:y=\frac{6x^{2}+8x+2}{\sqrt{x}}
derivative of-4x^{1/2}	derivative\:-4x^{\frac{1}{2}}
simplify x/2 ln((1+x)/(1-x))-1	simplify\:\frac{x}{2}\ln(\frac{1+x}{1-x})-1
(\partial)/(\partial x)((x-1)y^2e^{xy})	\frac{\partial\:}{\partial\:x}((x-1)y^{2}e^{xy})
(dy)/(dx)= y/(2x)	\frac{dy}{dx}=\frac{y}{2x}
sum from n=1 to infinity of (n!)/(n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n^{2}+1}
sum from n=1 to infinity of 0.8^n	\sum\:_{n=1}^{\infty\:}0.8^{n}
integral of (\sqrt[3]{x^5}+1/(3sqrt(x)))	\int\:(\sqrt[3]{x^{5}}+\frac{1}{3\sqrt{x}})dx
integral of (sec^2(x))	\int\:(\sec^{2}(x))dx
integral of sin^3(2x)*cos(2x)	\int\:\sin^{3}(2x)\cdot\:\cos(2x)dx
integral from 1 to infinity of 4/(x-1)	\int\:_{1}^{\infty\:}\frac{4}{x-1}dx
derivative of 800x-0.1x^2	derivative\:800x-0.1x^{2}
sum from n=1 to infinity of (9n)/(4n+9)	\sum\:_{n=1}^{\infty\:}\frac{9n}{4n+9}
derivative of 2/(1-3x)	\frac{d}{dx}(\frac{2}{1-3x})
limit as x approaches 0 of x/(sin(3x))	\lim\:_{x\to\:0}(\frac{x}{\sin(3x)})
slope of (-1,2),(-4,-1)	slope\:(-1,2),(-4,-1)
y^'+4y=cos(4t)	y^{\prime\:}+4y=\cos(4t)
(\partial)/(\partial y)(3x^2y^3)	\frac{\partial\:}{\partial\:y}(3x^{2}y^{3})
taylor 1/(1-x^2)	taylor\:\frac{1}{1-x^{2}}
integral of csc((v-pi)/2)cot((v-pi)/2)	\int\:\csc(\frac{v-π}{2})\cot(\frac{v-π}{2})dv
(dy)/(dx)+(4/x)y=-4x-5	\frac{dy}{dx}+(\frac{4}{x})y=-4x-5
integral from 0 to 1 of 1/(sqrt(x)(x+1))	\int\:_{0}^{1}\frac{1}{\sqrt{x}(x+1)}dx
(\partial)/(\partial x)(4x^4y^5-3x^2)	\frac{\partial\:}{\partial\:x}(4x^{4}y^{5}-3x^{2})
(\partial)/(\partial x)(x-y^2+3xy)	\frac{\partial\:}{\partial\:x}(x-y^{2}+3xy)
integral of (1/(x^2+9))	\int\:(\frac{1}{x^{2}+9})dx
derivative of y=((x-5))/(x^3)	derivative\:y=\frac{(x-5)}{x^{3}}
derivative of 1/(2x+2)	\frac{d}{dx}(\frac{1}{2x+2})
slope of (-3.3)(5.9)	slope\:(-3.3)(5.9)
(\partial)/(\partial y)(e^{2y})	\frac{\partial\:}{\partial\:y}(e^{2y})
integral of (2x)/(x^2+5)	\int\:\frac{2x}{x^{2}+5}dx
integral from 0 to 2 of (2x)/((x^2+5)^2)	\int\:_{0}^{2}\frac{2x}{(x^{2}+5)^{2}}dx
derivative of (ln(x)^{1/2})	\frac{d}{dx}((\ln(x))^{\frac{1}{2}})
derivative of (-x^2-1/((x^2-1)^2))	\frac{d}{dx}(\frac{-x^{2}-1}{(x^{2}-1)^{2}})
integral of e^{-t}*(-t^2+t-1)	\int\:e^{-t}\cdot\:(-t^{2}+t-1)dt
integral from 0 to 4 of (2+xsqrt(x))	\int\:_{0}^{4}(2+x\sqrt{x})dx
integral of 2(1-x)	\int\:2(1-x)dx
d/(dy)(e^y)	\frac{d}{dy}(e^{y})
integral of 2/3 x^{3/2}*1/x	\int\:\frac{2}{3}x^{\frac{3}{2}}\cdot\:\frac{1}{x}dx
integral of (xe^{-2x})	\int\:(xe^{-2x})dx
y^{''}+16y=0,y(0)=2,y^'(0)=1	y^{\prime\:\prime\:}+16y=0,y(0)=2,y^{\prime\:}(0)=1
(\partial)/(\partial x)(arcsin(5x))	\frac{\partial\:}{\partial\:x}(\arcsin(5x))
y^{''''}+4y^{''}=0	y^{\prime\:\prime\:\prime\:\prime\:}+4y^{\prime\:\prime\:}=0
limit as x approaches 1 of xln(x)-x	\lim\:_{x\to\:1}(x\ln(x)-x)
(\partial)/(\partial x)((x+y)e^y)	\frac{\partial\:}{\partial\:x}((x+y)e^{y})
integral of k/r (-(r^2)/4)	\int\:\frac{k}{r}(-\frac{r^{2}}{4})dr
integral of 1/(x^2sqrt(400-x^2))	\int\:\frac{1}{x^{2}\sqrt{400-x^{2}}}dx
derivative of (2x^3+4(x^4-4x))	\frac{d}{dx}((2x^{3}+4)(x^{4}-4x))
integral from 0 to 1 of 5/(sqrt(1-x^2))	\int\:_{0}^{1}\frac{5}{\sqrt{1-x^{2}}}dx
derivative of y=(x+5)(x^3-1)(x^2-x+3)	derivative\:y=(x+5)(x^{3}-1)(x^{2}-x+3)
derivative of 2e^{7x}	\frac{d}{dx}(2e^{7x})
integral of 1/(5-4sin(x)+3cos(x))	\int\:\frac{1}{5-4\sin(x)+3\cos(x)}dx
-4y^'+y=1	-4y^{\prime\:}+y=1
area e^x,-x+1,x=1	area\:e^{x},-x+1,x=1
derivative of (2x+5^2)	\frac{d}{dx}((2x+5)^{2})
derivative of 9e^x+2/(\sqrt[3]{x})	\frac{d}{dx}(9e^{x}+\frac{2}{\sqrt[3]{x}})
integral from-2 to 1 of (x-8\|x\|)	\int\:_{-2}^{1}(x-8\left\|x\right\|)dx
derivative of f(x)= x/(sqrt(2x+3))	derivative\:f(x)=\frac{x}{\sqrt{2x+3}}
derivative of sqrt(x^2-cx)	\frac{d}{dx}(\sqrt{x^{2}-cx})
derivative of 3/(2x^2)	\frac{d}{dx}(\frac{3}{2x^{2}})
ln(x)(dy)/(dx)+y/x =xln(x)	\ln(x)\frac{dy}{dx}+\frac{y}{x}=x\ln(x)
derivative of (3-5x^5)	\frac{d}{dx}((3-5x)^{5})
derivative of (x^4/(x-1))	\frac{d}{dx}(\frac{x^{4}}{x-1})
area x=(12-y^2)/4 ,x=y	area\:x=\frac{12-y^{2}}{4},x=y
y^'x+4yx=8,y(0)=1	y^{\prime\:}x+4yx=8,y(0)=1
integral of 1/((1+sin^2(x)))	\int\:\frac{1}{(1+\sin^{2}(x))}dx
derivative of x^2-x-2	derivative\:x^{2}-x-2
derivative of (10x+2^x)	\frac{d}{dx}((10x+2)^{x})
derivative of xy^3	derivative\:xy^{3}
implicit (dy)/(dx),y=x+1/x	implicit\:\frac{dy}{dx},y=x+\frac{1}{x}
derivative of (3x^2-1/(2x+5))	\frac{d}{dx}(\frac{3x^{2}-1}{2x+5})
sum from n=0 to infinity of 6(4/5)^n	\sum\:_{n=0}^{\infty\:}6(\frac{4}{5})^{n}
integral of (tan(ln(4x+2)))/(4x+2)	\int\:\frac{\tan(\ln(4x+2))}{4x+2}dx
derivative of (5sqrt(x)+3)x^2	derivative\:(5\sqrt{x}+3)x^{2}
sum from n=0 to infinity of (2/3)(5/4)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{3})(\frac{5}{4})^{n}
inverse oflaplace e^{-2s} 1/((s+1)^2)	inverselaplace\:e^{-2s}\frac{1}{(s+1)^{2}}
y^'=(x^2)/y	y^{\prime\:}=\frac{x^{2}}{y}
integral of 8/((x-2)(x^2+4))	\int\:\frac{8}{(x-2)(x^{2}+4)}dx
integral of sqrt(e^{6x)-4}	\int\:\sqrt{e^{6x}-4}dx
integral of y/(x^2+1)	\int\:\frac{y}{x^{2}+1}dx
derivative of 2000-4x	\frac{d}{dx}(2000-4x)
integral of 1/(sqrt(16x^2+9))	\int\:\frac{1}{\sqrt{16x^{2}+9}}dx
(x^2+xy)dx-x^2dy=0	(x^{2}+xy)dx-x^{2}dy=0
derivative of-xcos(x+cos(x))	\frac{d}{dx}(-x\cos(x)+\cos(x))
tangent of y=x^4+8x^2-x	tangent\:y=x^{4}+8x^{2}-x
integral of 4sin(2x)-3cos(3x)	\int\:4\cdot\:\sin(2x)-3\cdot\:\cos(3x)dx
integral of 15x^{17}e^{x^9}	\int\:15x^{17}e^{x^{9}}dx
limit as x approaches 4 of 3(x^2)/2	\lim\:_{x\to\:4}(3\frac{x^{2}}{2})
tangent of f(x)= 1/(x^5),(-3,-1/243)	tangent\:f(x)=\frac{1}{x^{5}},(-3,-\frac{1}{243})
integral from 1 to 3 of xln(x)	\int\:_{1}^{3}x\ln(x)dx
integral of (4-32x)/(sqrt(25-16x^2))	\int\:\frac{4-32x}{\sqrt{25-16x^{2}}}dx
derivative of sqrt(8+\sqrt{4x)}	\frac{d}{dx}(\sqrt{8+\sqrt{4x}})
integral of sqrt(x\sqrt{x\sqrt{x)}}	\int\:\sqrt{x\sqrt{x\sqrt{x}}}dx
tangent of f(x)=8(x-1/x)^3,\at x=2	tangent\:f(x)=8(x-\frac{1}{x})^{3},\at\:x=2
sum from n=0 to infinity of (3x)^n	\sum\:_{n=0}^{\infty\:}(3x)^{n}

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