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Popular Calculus Problems

derivative of (4sqrt(x)+1^2)	\frac{d}{dx}((4\sqrt{x}+1)^{2})
inverse oflaplace 6/(s^2+5s+4)	inverselaplace\:\frac{6}{s^{2}+5s+4}
derivative of 8sqrt(4x^2+7)	\frac{d}{dx}(8\sqrt{4x^{2}+7})
integral from-4 to 0 of 1/((x+2)^{1/3)}	\int\:_{-4}^{0}\frac{1}{(x+2)^{\frac{1}{3}}}dx
derivative of ((6e^x)/(2e^x+1))	\frac{d}{dx}(\frac{(6e^{x})}{2e^{x}+1})
tangent of 1/(2sqrt(x)),\at x=64	tangent\:\frac{1}{2\sqrt{x}},\at\:x=64
integral of 1/(xsqrt(121x^2-121))	\int\:\frac{1}{x\sqrt{121x^{2}-121}}dx
integral of y+x	\int\:y+xdx
limit as x approaches 3 of (\|3-x\|)/(x-3)	\lim\:_{x\to\:3}(\frac{\left\|3-x\right\|}{x-3})
(2x^3-3x+1)^'	(2x^{3}-3x+1)^{\prime\:}
derivative of y=(x^2-2x+7)sqrt(25-x^2)	derivative\:y=(x^{2}-2x+7)\sqrt{25-x^{2}}
limit as x approaches 5 of x-3	\lim\:_{x\to\:5}(x-3)
(\partial)/(\partial x)(in(x+2y+3z))	\frac{\partial\:}{\partial\:x}(in(x+2y+3z))
limit as x approaches 1 of 1/(1-x)	\lim\:_{x\to\:1}(\frac{1}{1-x})
integral of ((ln(x))^{48})/x	\int\:\frac{(\ln(x))^{48}}{x}dx
derivative of ln(3-5x)	derivative\:\ln(3-5x)
derivative of (3tan(x)/x)	\frac{d}{dx}(\frac{3\tan(x)}{x})
derivative of f(x)=((ax+b))/(cx+d)	derivative\:f(x)=\frac{(ax+b)}{cx+d}
derivative of 1/8 y^3	derivative\:\frac{1}{8}y^{3}
(d^2)/(dx^2)(5csc(x))	\frac{d^{2}}{dx^{2}}(5\csc(x))
maclaurin ln((sqrt(1+2x))/(1-3x))	maclaurin\:\ln(\frac{\sqrt{1+2x}}{1-3x})
slope of (4.5)(1.2)	slope\:(4.5)(1.2)
derivative of (x^3/(sin(x)))	\frac{d}{dx}(\frac{x^{3}}{\sin(x)})
tangent of y=x^2-2x+3,(2,3)	tangent\:y=x^{2}-2x+3,(2,3)
(\partial)/(\partial x)(7x)	\frac{\partial\:}{\partial\:x}(7x)
((x^2+1)dy)/(dx)+7x(y-1)=0	\frac{(x^{2}+1)dy}{dx}+7x(y-1)=0
integral of sqrt(x)*(3x+sqrt(x))	\int\:\sqrt{x}\cdot\:(3x+\sqrt{x})dx
(\partial)/(\partial x)(e^{4x})	\frac{\partial\:}{\partial\:x}(e^{4x})
laplacetransform t^2sin(5t)	laplacetransform\:t^{2}\sin(5t)
(\partial)/(\partial y)(y^2+2)	\frac{\partial\:}{\partial\:y}(y^{2}+2)
integral of-1/(e^{3x)}	\int\:-\frac{1}{e^{3x}}dx
integral of 5cos^3(5x)	\int\:5\cos^{3}(5x)dx
(\partial)/(\partial x)(cos^9(x^8y^6))	\frac{\partial\:}{\partial\:x}(\cos^{9}(x^{8}y^{6}))
derivative of 4^{c/x}	derivative\:4^{\frac{c}{x}}
integral of sin^3(xco)s^3x	\int\:\sin^{3}(xco)s^{3}xdx
integral from 0 to infinity of xe^{-x/9}	\int\:_{0}^{\infty\:}xe^{-\frac{x}{9}}dx
limit as x approaches infinity of-3	\lim\:_{x\to\:\infty\:}(-3)
(\partial)/(\partial x)((3x+2xy)/(7x+6y))	\frac{\partial\:}{\partial\:x}(\frac{3x+2xy}{7x+6y})
integral of 6tan^3(x)	\int\:6\tan^{3}(x)dx
laplacetransform 45t^2	laplacetransform\:45t^{2}
limit as x approaches 0 of x*ln(sin(x))	\lim\:_{x\to\:0}(x\cdot\:\ln(\sin(x)))
derivative of (4x/(sqrt(x^2+6)))	\frac{d}{dx}(\frac{4x}{\sqrt{x^{2}+6}})
ydx-(4x^2y+x)dy=0	ydx-(4x^{2}y+x)dy=0
derivative of ln(xe^{-7x})	\frac{d}{dx}(\ln(xe^{-7x}))
integral from 1.5 to 2.5 of 9800(7-y)(1)	\int\:_{1.5}^{2.5}9800(7-y)(1)dy
inverse oflaplace 1/(s^2+16)	inverselaplace\:\frac{1}{s^{2}+16}
inverse oflaplace 1/(s(s^2+s+5/4))	inverselaplace\:\frac{1}{s(s^{2}+s+\frac{5}{4})}
derivative of e^{x-1}	derivative\:e^{x-1}
(\partial)/(\partial x)(2xy+5x^2)	\frac{\partial\:}{\partial\:x}(2xy+5x^{2})
tangent of f(x)=(x^2)/(x+9),\at x=1	tangent\:f(x)=\frac{x^{2}}{x+9},\at\:x=1
limit as x approaches 0 of x/(x^2+5x)	\lim\:_{x\to\:0}(\frac{x}{x^{2}+5x})
derivative of y=x^4f(x)	derivative\:y=x^{4}f(x)
integral of 1/(x(1+ln(x))^4)	\int\:\frac{1}{x(1+\ln(x))^{4}}dx
inverse oflaplace 6/(2s+1)	inverselaplace\:\frac{6}{2s+1}
integral of cot(x)ln(sin(x))	\int\:\cot(x)\ln(\sin(x))dx
derivative of (x-2/(x^2+5x+4))	\frac{d}{dx}(\frac{x-2}{x^{2}+5x+4})
(dy)/(dx)=-y^{1/3}	\frac{dy}{dx}=-y^{\frac{1}{3}}
(d^3)/(dx^3)(e^{-x^2})	\frac{d^{3}}{dx^{3}}(e^{-x^{2}})
area y=2x^3,y=18x	area\:y=2x^{3},y=18x
tangent of f(x)=3x-2x^2,(-3,-27)	tangent\:f(x)=3x-2x^{2},(-3,-27)
limit as x approaches 0 of pi^2	\lim\:_{x\to\:0}(π^{2})
(d^2)/(dx^2)(((x-5)(x^2+5x+25))/(x^3))	\frac{d^{2}}{dx^{2}}(\frac{(x-5)(x^{2}+5x+25)}{x^{3}})
integral of (1+tan(x))^3sec^2(x)	\int\:(1+\tan(x))^{3}\sec^{2}(x)dx
integral of-1/2 cos(2t)	\int\:-\frac{1}{2}\cos(2t)dt
integral of 3sec(2x)tan(2x)	\int\:3\sec(2x)\tan(2x)dx
integral of xcos(7x)	\int\:x\cos(7x)dx
derivative of 3-2x	\frac{d}{dx}(3-2x)
limit as x approaches infinity of 1/4	\lim\:_{x\to\:\infty\:}(\frac{1}{4})
integral from 0 to N of e^{-st}cos(5t)	\int\:_{0}^{N}e^{-st}\cos(5t)dt
integral of 4/((x-6)^3)	\int\:\frac{4}{(x-6)^{3}}dx
100x+(dy)/(dx)=xy	100x+\frac{dy}{dx}=xy
limit as t approaches 10 of (t^2+3t-130)/(t^2-100)	\lim\:_{t\to\:10}(\frac{t^{2}+3t-130}{t^{2}-100})
derivative of (e^{-x}/(1+x^2))	\frac{d}{dx}(\frac{e^{-x}}{1+x^{2}})
integral of (sec(x))/((sec(x)-tan(x)))	\int\:\frac{\sec(x)}{(\sec(x)-\tan(x))}dx
y^'+2x=0	y^{\prime\:}+2x=0
(\partial)/(\partial t)(s^2t^2)	\frac{\partial\:}{\partial\:t}(s^{2}t^{2})
integral of (1+2x)^2	\int\:(1+2x)^{2}dx
derivative of (-3x-2)/(2x^2+x+3)	derivative\:\frac{-3x-2}{2x^{2}+x+3}
derivative of (e^x/(x^3))	\frac{d}{dx}(\frac{e^{x}}{x^{3}})
(\partial)/(\partial y)(-2xe^{xy})	\frac{\partial\:}{\partial\:y}(-2xe^{xy})
y^'=(x-14)^2	y^{\prime\:}=(x-14)^{2}
y^{''}+324y=sec(18x),y(0)=2,y^'(0)=-1	y^{\prime\:\prime\:}+324y=\sec(18x),y(0)=2,y^{\prime\:}(0)=-1
sum from n=3 to infinity of 3/(n^2-3n+2)	\sum\:_{n=3}^{\infty\:}\frac{3}{n^{2}-3n+2}
limit as x approaches 0 of ((1+x)^2)/x	\lim\:_{x\to\:0}(\frac{(1+x)^{2}}{x})
integral of ((ln(x))^2+1)/(ln(x))	\int\:\frac{(\ln(x))^{2}+1}{\ln(x)}dx
y^'=(e^{x-y})/(e^x+1)	y^{\prime\:}=\frac{e^{x-y}}{e^{x}+1}
(d^2y)/(dx^2)-5(dy)/(dx)+ky=0	\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+ky=0
y^'+3xe^y=0	y^{\prime\:}+3xe^{y}=0
sum from n=1 to infinity of (3^n)/(n2^n)	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{n2^{n}}
(\partial)/(\partial y)(arctan(y/x))	\frac{\partial\:}{\partial\:y}(\arctan(\frac{y}{x}))
y^{''}+18y^'+97y=0	y^{\prime\:\prime\:}+18y^{\prime\:}+97y=0
(\partial)/(\partial x)(arcsin(y/((x^2+y^2)^{1/2)}))	\frac{\partial\:}{\partial\:x}(\arcsin(\frac{y}{(x^{2}+y^{2})^{\frac{1}{2}}}))
integral of tan(x)-2sin(x)	\int\:\tan(x)-2\sin(x)dx
derivative of (300/x)	\frac{d}{dx}(\frac{300}{x})
(\partial)/(\partial x)(xyz)	\frac{\partial\:}{\partial\:x}(xyz)
simplify f(x)g(x)h(x)	simplify\:f(x)g(x)h(x)
derivative of ((\sqrt[3]{t}))/(t-3)	derivative\:\frac{(\sqrt[3]{t})}{t-3}
integral of-1/2	\int\:-\frac{1}{2}dx
integral from 0 to 1 of sqrt(x-x^2)	\int\:_{0}^{1}\sqrt{x-x^{2}}dx
integral of (y-1)(2y+1)	\int\:(y-1)(2y+1)dy

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