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Popular Calculus Problems

(dy)/(dt)=(15-(3y)/(360-2t))	\frac{dy}{dt}=(15-\frac{3y}{360-2t})
(\partial)/(\partial v)(ucos(v))	\frac{\partial\:}{\partial\:v}(u\cos(v))
derivative of f(x)=2x^2-6x	derivative\:f(x)=2x^{2}-6x
integral from-pi to 2pi of cos^2(x)	\int\:_{-π}^{2π}\cos^{2}(x)dx
limit as x approaches 0 of e^{1/x ln(1+x^2)}	\lim\:_{x\to\:0}(e^{\frac{1}{x}\ln(1+x^{2})})
(\partial)/(\partial x)(ln(x/(x+2)))	\frac{\partial\:}{\partial\:x}(\ln(\frac{x}{x+2}))
integral of (3x^2-2)/(x^2-2x-8)	\int\:\frac{3x^{2}-2}{x^{2}-2x-8}dx
integral of (y-4)^2	\int\:(y-4)^{2}dy
derivative of (x^2/(x-6))	\frac{d}{dx}(\frac{x^{2}}{x-6})
(\partial)/(\partial x)((xy)/(sqrt(1+xy^2)))	\frac{\partial\:}{\partial\:x}(\frac{xy}{\sqrt{1+xy^{2}}})
integral of ((sin(x))^2)/((cos(x))^4)	\int\:\frac{(\sin(x))^{2}}{(\cos(x))^{4}}dx
integral from 1 to 4 of (e^{4/x})/(x^2)	\int\:_{1}^{4}\frac{e^{\frac{4}{x}}}{x^{2}}dx
derivative of ae^{2x}+be^x	\frac{d}{dx}(ae^{2x}+be^{x})
(\partial)/(\partial z)(e^xsin(yz))	\frac{\partial\:}{\partial\:z}(e^{x}\sin(yz))
integral of 10sin^3(x)cos^7(x)	\int\:10\sin^{3}(x)\cos^{7}(x)dx
(\partial)/(\partial x)(y^2-e^{xy})	\frac{\partial\:}{\partial\:x}(y^{2}-e^{xy})
inverse oflaplace s/(s^4+1)	inverselaplace\:\frac{s}{s^{4}+1}
integral of tan(2t)	\int\:\tan(2t)dt
y^{''}+16y=te^{4t}	y^{\prime\:\prime\:}+16y=te^{4t}
derivative of y/x	derivative\:\frac{y}{x}
((100)/(log_{10)(2x+1)})^'	(\frac{100}{\log_{10}(2x+1)})^{\prime\:}
f(x)=x^3e^{2x}	f(x)=x^{3}e^{2x}
limit as x approaches 1 of x^{3/(1-x)}	\lim\:_{x\to\:1}(x^{\frac{3}{1-x}})
y^{''}-5y^'-6y=0,y(0)=5,y^'(0)=12	y^{\prime\:\prime\:}-5y^{\prime\:}-6y=0,y(0)=5,y^{\prime\:}(0)=12
integral of 1/(10x^{1/2)-x}	\int\:\frac{1}{10x^{\frac{1}{2}}-x}dx
integral of 1/((1-x)^2)	\int\:\frac{1}{(1-x)^{2}}dx
integral of (3y^2-t^2)/(y^5)	\int\:\frac{3y^{2}-t^{2}}{y^{5}}dy
derivative of ln(9x^2)	\frac{d}{dx}(\ln(9)x^{2})
limit as x approaches-8-of (-5x)/(x+8)	\lim\:_{x\to\:-8-}(\frac{-5x}{x+8})
integral from 3 to 9 of (1+x^2)	\int\:_{3}^{9}(1+x^{2})dx
integral of (24)/((x-2)(x^2+4))	\int\:\frac{24}{(x-2)(x^{2}+4)}dx
integral from 0 to 1 of (x^2)/(x^3-1)	\int\:_{0}^{1}\frac{x^{2}}{x^{3}-1}dx
derivative of y=e^{5x}	derivative\:y=e^{5x}
maclaurin ln(cos(x))	maclaurin\:\ln(\cos(x))
limit as x approaches 2 of x^2-5x+6	\lim\:_{x\to\:2}(x^{2}-5x+6)
derivative of (7x^2-12x)e^x	derivative\:(7x^{2}-12x)e^{x}
derivative of x^3(4-x)	\frac{d}{dx}(x^{3}(4-x))
sum from n=0 to infinity of 4/(n(n+2))	\sum\:_{n=0}^{\infty\:}\frac{4}{n(n+2)}
sum from n=0 to infinity of ((5^n))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(5^{n})}{n!}
derivative of tan^2(θ)	derivative\:\tan^{2}(θ)
integral of (w^2)/((w^2+7)^2)	\int\:\frac{w^{2}}{(w^{2}+7)^{2}}dw
y^'=-(2x)/y ,y(1)=10	y^{\prime\:}=-\frac{2x}{y},y(1)=10
derivative of y=(arctan(7x))^2	derivative\:y=(\arctan(7x))^{2}
limit as x approaches 8 of x^{-1}	\lim\:_{x\to\:8}(x^{-1})
d/(du)(e^ucos(v))	\frac{d}{du}(e^{u}\cos(v))
maclaurin 2sin(3x)	maclaurin\:2\sin(3x)
derivative of 3(cos(x)ln(x)+(sin(x))/x)	derivative\:3(\cos(x)\ln(x)+\frac{\sin(x)}{x})
derivative of ln(sqrt(4+x^2))	\frac{d}{dx}(\ln(\sqrt{4+x^{2}}))
integral of 16tan^3(x)sec(x)	\int\:16\tan^{3}(x)\sec(x)dx
limit as x approaches-1 of (x^4-1)/(x+1)	\lim\:_{x\to\:-1}(\frac{x^{4}-1}{x+1})
limit as x approaches 0-of (1-1/x)^x	\lim\:_{x\to\:0-}((1-\frac{1}{x})^{x})
derivative of x^3ln(7x)	\frac{d}{dx}(x^{3}\ln(7x))
derivative of f(x)=e^{4-5x}(3x^3-2)^6	derivative\:f(x)=e^{4-5x}(3x^{3}-2)^{6}
y^'=2x+y,y(0)=9	y^{\prime\:}=2x+y,y(0)=9
y^{''}-y=10sin^2(x)	y^{\prime\:\prime\:}-y=10\sin^{2}(x)
integral of 2^x(2^{-x}+1)	\int\:2^{x}(2^{-x}+1)dx
integral of 1/(x^2+100)	\int\:\frac{1}{x^{2}+100}dx
sum from n=0 to infinity of (1/10)^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{10})^{n}
laplacetransform 5cos(t/(3000))	laplacetransform\:5\cos(\frac{t}{3000})
integral of e^{-X}	\int\:e^{-X}dX
integral of 3+csc(x)*cot(x)	\int\:3+\csc(x)\cdot\:\cot(x)dx
f(x)=(1+x)/(1+e^x)	f(x)=\frac{1+x}{1+e^{x}}
f(x)=sec^3(x)	f(x)=\sec^{3}(x)
2(d^2y)/(dx^2)+2(dy)/(dx)+3y=0	2\frac{d^{2}y}{dx^{2}}+2\frac{dy}{dx}+3y=0
sum from n=0 to infinity of 83(1/100)^n	\sum\:_{n=0}^{\infty\:}83(\frac{1}{100})^{n}
limit as x approaches 4-of 3-x	\lim\:_{x\to\:4-}(3-x)
derivative of (8x^4-9x^2+4)^4	derivative\:(8x^{4}-9x^{2}+4)^{4}
limit as x approaches 0 of (tan^2(x))/x	\lim\:_{x\to\:0}(\frac{\tan^{2}(x)}{x})
18y^{''}+3y^'-10y=0	18y^{\prime\:\prime\:}+3y^{\prime\:}-10y=0
integral of x^4(x^3+8x^2+7)	\int\:x^{4}(x^{3}+8x^{2}+7)dx
derivative of 1/(2x+1)	derivative\:\frac{1}{2x+1}
(\partial)/(\partial x)(-1/(sqrt(x^2+y^2)))	\frac{\partial\:}{\partial\:x}(-\frac{1}{\sqrt{x^{2}+y^{2}}})
derivative of f(x)=tan^3(x+csc(x))	derivative\:f(x)=\tan^{3}(x+\csc(x))
tangent of y=4-x^2	tangent\:y=4-x^{2}
derivative of (\sqrt[5]{x^2}/(x^2+1))	\frac{d}{dx}(\frac{\sqrt[5]{x^{2}}}{x^{2}+1})
integral of (\sqrt[15]{x^{13}})	\int\:(\sqrt[15]{x^{13}})dx
integral of 9x^2-4x+3	\int\:9x^{2}-4x+3dx
limit as p approaches 4 of sqrt(p^2+p+5)	\lim\:_{p\to\:4}(\sqrt{p^{2}+p+5})
derivative of e^{2x}cos(5x)	derivative\:e^{2x}\cos(5x)
derivative of f(x)=(6x)/(3+x)	derivative\:f(x)=\frac{6x}{3+x}
derivative of sqrt(144-x^2)	\frac{d}{dx}(\sqrt{144-x^{2}})
derivative of 1+x	derivative\:1+x
xy^'-y= 2/3 xln(x)	xy^{\prime\:}-y=\frac{2}{3}x\ln(x)
derivative of x^{2.4}+e^{2.4}	derivative\:x^{2.4}+e^{2.4}
limit as x approaches 4-of (15)/(x-4)	\lim\:_{x\to\:4-}(\frac{15}{x-4})
area y=20+x-x^2,x^2-5x	area\:y=20+x-x^{2},x^{2}-5x
integral of (3x^5-2x^3)	\int\:(3x^{5}-2x^{3})dx
derivative of cos(tan(x))	derivative\:\cos(\tan(x))
(\partial)/(\partial x)(e^x-xy^3)	\frac{\partial\:}{\partial\:x}(e^{x}-xy^{3})
derivative of y=-2x^2	derivative\:y=-2x^{2}
derivative of (x^2)/(3+4x)	derivative\:\frac{x^{2}}{3+4x}
laplacetransform te^{-3t}sin(5t)	laplacetransform\:t\cdot\:e^{-3t}\cdot\:\sin(5t)
derivative of (x^2)/(5+sqrt(x))	derivative\:\frac{x^{2}}{5+\sqrt{x}}
derivative of-1/((x-1)^2)	derivative\:-\frac{1}{(x-1)^{2}}
integral of 2sin(x)+cos(x)-3	\int\:2\sin(x)+\cos(x)-3dx
d/(dy)(e^{-y})	\frac{d}{dy}(e^{-y})
inverse oflaplace x^{1/2}	inverselaplace\:x^{\frac{1}{2}}
derivative of y=5e^{(6x+7)}	derivative\:y=5e^{(6x+7)}
integral of e^{-x}(1+e^{-x})^3	\int\:e^{-x}(1+e^{-x})^{3}dx
derivative of 0.01x^2	\frac{d}{dx}(0.01x^{2})

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