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Popular Calculus Problems

derivative of tan(x/y)	\frac{d}{dx}(\tan(\frac{x}{y}))
sum from n=1 to infinity of 2/(4^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{2}{4^{2n}}
limit as h approaches 0 of ((7/(x+h)-7/x))/h	\lim\:_{h\to\:0}(\frac{(\frac{7}{x+h}-\frac{7}{x})}{h})
limit as x approaches 1 of ln\|x-1\|	\lim\:_{x\to\:1}(\ln\left\|x-1\right\|)
(\partial ^2)/(\partial x^2)(2cos(xy^2))	\frac{\partial\:^{2}}{\partial\:x^{2}}(2\cos(xy^{2}))
((dy)/(dx))=(x+y+7)^2	(\frac{dy}{dx})=(x+y+7)^{2}
-(xsqrt(1-y^2))/(ysqrt(1-x^2))=(dy)/(dx)	-\frac{x\sqrt{1-y^{2}}}{y\sqrt{1-x^{2}}}=\frac{dy}{dx}
sum from n=0 to infinity of (n^2+1)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{n^{2}+1}{n!}
integral of sin(3x)cos(3x)	\int\:\sin(3x)\cos(3x)dx
d/(du)(sqrt((u-1)/(u+1)))	\frac{d}{du}(\sqrt{\frac{u-1}{u+1}})
(d^2y)/(dx^2)-(dy)/(dx)-30y=0	\frac{d^{2}y}{dx^{2}}-\frac{dy}{dx}-30y=0
derivative of sin^3(cos(7x^2))	\frac{d}{dx}(\sin^{3}(\cos(7x^{2})))
integral of 1/(4sin^2(x))	\int\:\frac{1}{4\sin^{2}(x)}dx
(dy)/(dt)-2y=3e^t	\frac{dy}{dt}-2y=3e^{t}
integral of sin^2(5x)cos^4(5x)	\int\:\sin^{2}(5x)\cos^{4}(5x)dx
integral from-3 to 3 of 9x^2	\int\:_{-3}^{3}9x^{2}dx
y^{''}-6y^'+9y=6x^2e^{3x}	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=6x^{2}e^{3x}
integral of 1/(10x^4)	\int\:\frac{1}{10x^{4}}dx
derivative of (10/((x+5)^2))	\frac{d}{dx}(\frac{10}{(x+5)^{2}})
taylor x*sin(x)	taylor\:x\cdot\:\sin(x)
integral of (3(-5+ln(4x))^3)/x	\int\:\frac{3(-5+\ln(4x))^{3}}{x}dx
tangent of f(x)=x^2-9x+18,4,\at x=3	tangent\:f(x)=x^{2}-9x+18,4,\at\:x=3
derivative of x/((3x-8^8))	\frac{d}{dx}(\frac{x}{(3x-8)^{8}})
inverse oflaplace (4s)/(s^2+16)	inverselaplace\:\frac{4s}{s^{2}+16}
tangent of f(x)= 3/(x+3),\at x=-1/3	tangent\:f(x)=\frac{3}{x+3},\at\:x=-\frac{1}{3}
area y=x^2,y=8-2x	area\:y=x^{2},y=8-2x
limit as x approaches 0 of cos(x)*x	\lim\:_{x\to\:0}(\cos(x)\cdot\:x)
(d^4)/(dx^4)(2ln(x))	\frac{d^{4}}{dx^{4}}(2\ln(x))
inverse oflaplace (20)/(s(s+30))	inverselaplace\:\frac{20}{s(s+30)}
integral of 2cos(t)+sec^2(t)	\int\:2\cos(t)+\sec^{2}(t)dt
(\partial)/(\partial x)(ln((1-T)wx))	\frac{\partial\:}{\partial\:x}(\ln((1-T)\cdot\:w\cdot\:x))
(dy)/(dx)+2y=4x	\frac{dy}{dx}+2y=4x
derivative of 9pi^3	derivative\:9π^{3}
derivative of arcsin(2x)	derivative\:\arcsin(2x)
tangent of f(x)=x^4-2x^2,\at x=1	tangent\:f(x)=x^{4}-2x^{2},\at\:x=1
limit as x approaches 0+of 1/x-cot(x)	\lim\:_{x\to\:0+}(\frac{1}{x}-\cot(x))
integral of (5f(x))/(x^2(x+1)^3)	\int\:\frac{5f(x)}{x^{2}(x+1)^{3}}dx
integral from 0 to pi of sin(nx)	\int\:_{0}^{π}\sin(nx)dx
derivative of (-cos(x))/(4x^2+2x-3)	derivative\:\frac{-\cos(x)}{4x^{2}+2x-3}
(\partial)/(\partial y)(ln(x+y^3))	\frac{\partial\:}{\partial\:y}(\ln(x+y^{3}))
(dy)/(dt)=4y	\frac{dy}{dt}=4y
sum from n=1 to infinity of (n+1)/(2n+1)	\sum\:_{n=1}^{\infty\:}\frac{n+1}{2n+1}
derivative of y= 5/(4x+1)	derivative\:y=\frac{5}{4x+1}
derivative of y=x^{3*7}	derivative\:y=x^{3\cdot\:7}
derivative of f(x)=((x^2-3x))/2	derivative\:f(x)=\frac{(x^{2}-3x)}{2}
(\partial)/(\partial x)(x^2+y^2+xy+3)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+xy+3)
(dy}{dx}=\frac{sqrt(x^2-9))/x	\frac{dy}{dx}=\frac{\sqrt{x^{2}-9}}{x}
integral from 0 to 3 of xe^{-4x}	\int\:_{0}^{3}xe^{-4x}dx
derivative of y=5e^x+7ln(x)	derivative\:y=5e^{x}+7\ln(x)
(\partial)/(\partial x)(1+x^3+x^4)	\frac{\partial\:}{\partial\:x}(1+x^{3}+x^{4})
derivative of 7/(x^2-x+2)	\frac{d}{dx}(\frac{7}{x^{2}-x+2})
y^{''}-y^'-6y=2e^t-t^2-2t+3	y^{\prime\:\prime\:}-y^{\prime\:}-6y=2e^{t}-t^{2}-2t+3
integral of 20-0.1	\int\:20-0.1
d/(dy)(4e^{2y}(2x^2+4x+2y+1))	\frac{d}{dy}(4e^{2y}(2x^{2}+4x+2y+1))
integral of ((ln(x^3)))/x	\int\:\frac{(\ln(x^{3}))}{x}dx
limit as x approaches infinity of x/(5x)	\lim\:_{x\to\:\infty\:}(\frac{x}{5x})
(\partial)/(\partial x)((y+cx),(x+k))	\frac{\partial\:}{\partial\:x}((y+cx),(x+k))
limit as x approaches infinity of 1/(6x)	\lim\:_{x\to\:\infty\:}(\frac{1}{6x})
derivative of (-x^2+9^2)	\frac{d}{dx}((-x^{2}+9)^{2})
(\partial)/(\partial v)(x^5v^2+2y^3u-3)	\frac{\partial\:}{\partial\:v}(x^{5}v^{2}+2y^{3}u-3)
integral of 2^{x/2}	\int\:2^{\frac{x}{2}}dx
x*(dy)/(dx)=2xe^x-y+6x^2	x\cdot\:\frac{dy}{dx}=2xe^{x}-y+6x^{2}
d/(dy)(-xysin(x)+2ycos(x))	\frac{d}{dy}(-xy\sin(x)+2y\cos(x))
y^{''}+y=tan^2(x)	y^{\prime\:\prime\:}+y=\tan^{2}(x)
x^2y^{''}-2xy^'+2y=x^2	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}+2y=x^{2}
derivative of f(x)=(x^2+5x+6)/(x^2-4)	derivative\:f(x)=\frac{x^{2}+5x+6}{x^{2}-4}
integral of x/(x^4-1)	\int\:\frac{x}{x^{4}-1}dx
derivative of-2e^{-x}cos(x)	\frac{d}{dx}(-2e^{-x}\cos(x))
y^'+2y=0,y(0)=1	y^{\prime\:}+2y=0,y(0)=1
4y^{''}+4y^'+17=0	4y^{\prime\:\prime\:}+4y^{\prime\:}+17=0
derivative of (x+7/(4x^2e^x))	\frac{d}{dx}(\frac{x+7}{4x^{2}e^{x}})
integral of arcsin(4/3 x+5)	\int\:\arcsin(\frac{4}{3}x+5)dx
tangent of (x^3+2)^5,\at x=-1	tangent\:(x^{3}+2)^{5},\at\:x=-1
(\partial)/(\partial x)(56y^4x^6-42y^3x^5)	\frac{\partial\:}{\partial\:x}(56y^{4}x^{6}-42y^{3}x^{5})
derivative of (x-1)^2(x-2)^3	derivative\:(x-1)^{2}(x-2)^{3}
sum from n=1 to infinity of 8((1/5)^n)	\sum\:_{n=1}^{\infty\:}8((\frac{1}{5})^{n})
limit as x approaches 0 of 6/x-6/(x^2-x)	\lim\:_{x\to\:0}(\frac{6}{x}-\frac{6}{x^{2}-x})
integral from 1 to 9 of 1/(9-sqrt(x))	\int\:_{1}^{9}\frac{1}{9-\sqrt{x}}dx
d/(d{y)}({y}{z}e^{{x}{z}})	\frac{d}{d{y}}({y}{z}e^{{x}{z}})
integral of-32x+64	\int\:-32x+64dx
derivative of ln(5t)	derivative\:\ln(5t)
x(d^2y)/(dx^2)-4x(dy)/(dx)=x^4	x\frac{d^{2}y}{dx^{2}}-4x\frac{dy}{dx}=x^{4}
derivative of 7^{3x}	\frac{d}{dx}(7^{3x})
integral of e^{-x}*e^{-iwx}	\int\:e^{-x}\cdot\:e^{-iwx}dx
integral from 1 to 100 of 1/(x^3)	\int\:_{1}^{100}\frac{1}{x^{3}}dx
integral of sqrt(sin(x))cos^3(x)	\int\:\sqrt{\sin(x)}\cos^{3}(x)dx
y^'+6(tan(6x))y=-2cos(6x)	y^{\prime\:}+6(\tan(6x))y=-2\cos(6x)
(dy)/(dx)= x/(sin(y))-9/(sin(y))	\frac{dy}{dx}=\frac{x}{\sin(y)}-\frac{9}{\sin(y)}
integral from 1 to 2y of y/x	\int\:_{1}^{2y}\frac{y}{x}dx
maclaurin 3cos(2x)	maclaurin\:3\cos(2x)
limit as x approaches 2 of \sqrt[6]{x-2}	\lim\:_{x\to\:2}(\sqrt[6]{x-2})
integral from 0 to 3 of sqrt(x+1)	\int\:_{0}^{3}\sqrt{x+1}dx
sum from n=0 to infinity of 9/4 (1/4)^n	\sum\:_{n=0}^{\infty\:}\frac{9}{4}(\frac{1}{4})^{n}
taylor tan(x),3	taylor\:\tan(x),3
(\partial)/(\partial x)(8xy^2z^3)	\frac{\partial\:}{\partial\:x}(8xy^{2}z^{3})
inverse oflaplace 4/(2(s-1)^2+50)	inverselaplace\:\frac{4}{2(s-1)^{2}+50}
derivative of 12sec(x)	\frac{d}{dx}(12\sec(x))
integral of (sin(x))/(cos(x)+cos^2(x))	\int\:\frac{\sin(x)}{\cos(x)+\cos^{2}(x)}dx
area 4x^2-4,x^8-1	area\:4x^{2}-4,x^{8}-1
(\partial)/(\partial x)(y+3xz+x^3)	\frac{\partial\:}{\partial\:x}(y+3xz+x^{3})

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