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Popular Calculus Problems

derivative of (10x+20)/x	derivative\:\frac{10x+20}{x}
integral of tan^3(6x)sec(6x)	\int\:\tan^{3}(6x)\sec(6x)dx
integral of sqrt(y^2-x^2)	\int\:\sqrt{y^{2}-x^{2}}dx
limit as x approaches-2 of sqrt(25-5x)	\lim\:_{x\to\:-2}(\sqrt{25-5x})
derivative of f(x)=x^{4/3}-4x^{1/3}+1	derivative\:f(x)=x^{\frac{4}{3}}-4x^{\frac{1}{3}}+1
integral from 0 to pi of sin(θ)	\int\:_{0}^{π}\sin(θ)dθ
derivative of x^2sqrt(5-x)	\frac{d}{dx}(x^{2}\sqrt{5-x})
derivative of x^4sec(5/x)	derivative\:x^{4}\sec(\frac{5}{x})
limit as z approaches 0 of 1/(f(z) 1/z)	\lim\:_{z\to\:0}(\frac{1}{f(z)\frac{1}{z}})
derivative of sqrt(x+4)	derivative\:\sqrt{x+4}
sum from n=1 to infinity of nsin(pin)	\sum\:_{n=1}^{\infty\:}n\cdot\:\sin(π\cdot\:n)
derivative of x^{sec(x})	\frac{d}{dx}(x^{\sec(x)})
integral of (ln(ln(5x)))/(5x)	\int\:\frac{\ln(\ln(5x))}{5x}dx
derivative of (x^2+6)^9	derivative\:(x^{2}+6)^{9}
(\partial)/(\partial z)(-xy)	\frac{\partial\:}{\partial\:z}(-xy)
ty^{''}+y^'=0	ty^{\prime\:\prime\:}+y^{\prime\:}=0
tangent of f(x)=7x-4x^2,(-3,-57)	tangent\:f(x)=7x-4x^{2},(-3,-57)
derivative of e^x(2x^4-1)	\frac{d}{dx}(e^{x}(2x^{4}-1))
(d^2)/(dx^2)(2x)	\frac{d^{2}}{dx^{2}}(2x)
integral of sqrt(x)*ln(x)	\int\:\sqrt{x}\cdot\:\ln(x)dx
integral from-4 to 0 of (1+sqrt(16-x^2))	\int\:_{-4}^{0}(1+\sqrt{16-x^{2}})dx
integral of t^2sqrt(13t-1)	\int\:t^{2}\sqrt{13t-1}dt
derivative of f(x)=(4/x)+(1/(5x^3+2x))	derivative\:f(x)=(\frac{4}{x})+(\frac{1}{5x^{3}+2x})
integral from 0 to pi/2 of sec^2(x/2)	\int\:_{0}^{\frac{π}{2}}\sec^{2}(\frac{x}{2})dx
xy^'-2y=0	xy^{\prime\:}-2y=0
y^'+y=4x	y^{\prime\:}+y=4x
integral of 2x+1/(x^2)+2x-3	\int\:2x+\frac{1}{x^{2}}+2x-3dx
taylor 1/(2x),1	taylor\:\frac{1}{2x},1
derivative of cos((ln(x+1)^2-e^{x^2}))	\frac{d}{dx}(\cos((\ln(x+1))^{2}-e^{x^{2}}))
(\partial)/(\partial x)(2x^{1/2}y^{1/4})	\frac{\partial\:}{\partial\:x}(2x^{\frac{1}{2}}y^{\frac{1}{4}})
derivative of x^3-(x^2)/(40)	derivative\:x^{3}-\frac{x^{2}}{40}
y^'=4+2sin(x/4)-y/(100)	y^{\prime\:}=4+2\sin(\frac{x}{4})-\frac{y}{100}
integral of 1/(n(ln(n))^2)	\int\:\frac{1}{n(\ln(n))^{2}}
integral from 0 to 1 of (3-4x)e^{2x}	\int\:_{0}^{1}(3-4x)e^{2x}dx
y^{''}+200/8*y=30sin(2x),y(0)=2,y^'(0)=0	y^{\prime\:\prime\:}+\frac{200}{8}\cdot\:y=30\sin(2x),y(0)=2,y^{\prime\:}(0)=0
derivative of-c/(x^2)	\frac{d}{dx}(-\frac{c}{x^{2}})
tangent of (2x+1)/(x+2)	tangent\:\frac{2x+1}{x+2}
laplacetransform 3t^4e^{-2t}	laplacetransform\:3t^{4}e^{-2t}
area x^5,e^3x^2	area\:x^{5},e^{3}x^{2}
inverse oflaplace (2s-3)/(s^2+4)	inverselaplace\:\frac{2s-3}{s^{2}+4}
y^'+xy=1xy^3	y^{\prime\:}+xy=1xy^{3}
integral from 1 to 6 of-x^2+7x-6	\int\:_{1}^{6}-x^{2}+7x-6dx
limit as x approaches 2+of (6x)/(x-2)	\lim\:_{x\to\:2+}(\frac{6x}{x-2})
(\partial)/(\partial x)(ln(1+x^2)-2e^{5y})	\frac{\partial\:}{\partial\:x}(\ln(1+x^{2})-2e^{5y})
integral of 1/(x(ln(x))^p)	\int\:\frac{1}{x(\ln(x))^{p}}dx
d/(d{y)}(c{y}^{-6})	\frac{d}{d{y}}(c{y}^{-6})
limit as x approaches 0 of cos(x)-sin(x)	\lim\:_{x\to\:0}(\cos(x)-\sin(x))
derivative of (e^x/(5x))	\frac{d}{dx}(\frac{e^{x}}{5x})
integral of-3arcsin(10x)	\int\:-3\arcsin(10x)dx
slope ofintercept (-5,-2),(5,4)	slopeintercept\:(-5,-2),(5,4)
integral of arcsin(x)x	\int\:\arcsin(x)xdx
limit as x approaches-3 of 2x^3+5x^2-25	\lim\:_{x\to\:-3}(2x^{3}+5x^{2}-25)
y^'=(2y)/x ,y(1)=2	y^{\prime\:}=\frac{2y}{x},y(1)=2
integral from 0 to 1 of x/(e^{2x)}	\int\:_{0}^{1}\frac{x}{e^{2x}}dx
derivative of-9.8x^2+2x+1	derivative\:-9.8x^{2}+2x+1
xy^'+5y=7x^2	xy^{\prime\:}+5y=7x^{2}
integral from 1 to 2 of 4/(2x+3)	\int\:_{1}^{2}\frac{4}{2x+3}dx
laplacetransform 2(t-2)	laplacetransform\:2(t-2)
integral of 1/(sqrt(16x^2-24x-27))	\int\:\frac{1}{\sqrt{16x^{2}-24x-27}}dx
derivative of x/5	derivative\:\frac{x}{5}
derivative of y=7cos(x)	derivative\:y=7\cos(x)
integral of t^2*ln^2(t)	\int\:t^{2}\cdot\:\ln^{2}(t)dt
limit as x approaches 0 of x^{-3}	\lim\:_{x\to\:0}(x^{-3})
derivative of 4x^{-1/3}+9/(x^{5/3})	\frac{d}{dx}(4x^{-\frac{1}{3}}+\frac{9}{x^{\frac{5}{3}}})
implicit (dy)/(dx),xcos(2x+3y)=ysin(x)	implicit\:\frac{dy}{dx},x\cos(2x+3y)=y\sin(x)
integral of 2sqrt(t)-t-9/(t^2)	\int\:2\sqrt{t}-t-\frac{9}{t^{2}}dt
limit as x approaches 0 of x^2-4	\lim\:_{x\to\:0}(x^{2}-4)
integral of (x^2)/((1-y^2))	\int\:\frac{x^{2}}{(1-y^{2})}
roots e^{ax}	roots\:e^{ax}
integral of (4/x-(16)/(x^2))	\int\:(\frac{4}{x}-\frac{16}{x^{2}})dx
(\partial)/(\partial y)((e^y)/(x+y^9))	\frac{\partial\:}{\partial\:y}(\frac{e^{y}}{x+y^{9}})
derivative of 2^{-2x}	\frac{d}{dx}(2^{-2x})
f(x)=cos(x)-sin(x)	f(x)=\cos(x)-\sin(x)
sum from n=0 to infinity of (2n)/n x^n	\sum\:_{n=0}^{\infty\:}\frac{2n}{n}x^{n}
(\partial)/(\partial x)(e^xsin(y+z)-z)	\frac{\partial\:}{\partial\:x}(e^{x}\sin(y+z)-z)
limit as x approaches 4 of 3-2	\lim\:_{x\to\:4}(3-2)
f(x)=sqrt(4-x)	f(x)=\sqrt{4-x}
integral of ((sec(x)+cos(x)))/(5cos(x))	\int\:\frac{(\sec(x)+\cos(x))}{5\cos(x)}dx
integral of cos^3(x)sin^5(x)	\int\:\cos^{3}(x)\sin^{5}(x)dx
tangent of y=x^2-3,(2,1)	tangent\:y=x^{2}-3,(2,1)
tangent of y=sqrt(5x+30),-1	tangent\:y=\sqrt{5x+30},-1
limit as x approaches 1 of (10)/(x-1)	\lim\:_{x\to\:1}(\frac{10}{x-1})
integral of x/2+3	\int\:\frac{x}{2}+3dx
derivative of (x^2-9/(x+3))	\frac{d}{dx}(\frac{x^{2}-9}{x+3})
derivative of 7xsin(x)+x^2e^x	derivative\:7x\cdot\:\sin(x)+x^{2}\cdot\:e^{x}
derivative of 1/(3x^2-5/(2x))	\frac{d}{dx}(\frac{1}{3x^{2}}-\frac{5}{2x})
x^2y^'-4xy=sin(2x)x^6	x^{2}y^{\prime\:}-4xy=\sin(2x)x^{6}
derivative of sqrt(a+bx)	\frac{d}{dx}(\sqrt{a+bx})
derivative of (2xe^x/(x^2+1))	\frac{d}{dx}(\frac{2xe^{x}}{x^{2}+1})
integral of 7x^2sin(2x)	\int\:7x^{2}\sin(2x)dx
sum from k=1 to infinity of (1/2)^k	\sum\:_{k=1}^{\infty\:}(\frac{1}{2})^{k}
derivative of (x^2/(64)+(y^2)/(25))=1	\frac{d}{dx}(\frac{x^{2}}{64}+\frac{y^{2}}{25})=1
limit as x approaches 2-of (-1)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{-1}{x^{2}-4})
integral of (14x-1)/((4x+1)(x-2))	\int\:\frac{14x-1}{(4x+1)(x-2)}dx
integral of 2xcos(-4x)	\int\:2x\cos(-4x)dx
derivative of sqrt(x+ln(3x))	\frac{d}{dx}(\sqrt{x+\ln(3x)})
integral from 0 to 1 of 2(1+sqrt(x))^6	\int\:_{0}^{1}2(1+\sqrt{x})^{6}dx
integral of 1/((x+1)^2(x-4))	\int\:\frac{1}{(x+1)^{2}(x-4)}dx
integral of x^{-1/2}	\int\:x^{-\frac{1}{2}}dx
(\partial)/(\partial x)(3x^2y^3-3x^2)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{3}-3x^{2})

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