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Popular Calculus Problems

derivative of 6x^{70}	\frac{d}{dx}(6x^{70})
integral of 1/(5x+16)	\int\:\frac{1}{5x+16}dx
area y=9x^2,y=x^2+7	area\:y=9x^{2},y=x^{2}+7
limit as h approaches 0 of 2xh	\lim\:_{h\to\:0}(2xh)
sum from n=5 to infinity of 1/(n^2)	\sum\:_{n=5}^{\infty\:}\frac{1}{n^{2}}
integral of (1/y sin(x/y)+x)	\int\:(\frac{1}{y}\sin(\frac{x}{y})+x)dx
derivative of arctan(e^x+1)	\frac{d}{dx}(\arctan(e^{x}+1))
integral from-1 to 2 of (x^2-x-2)	\int\:_{-1}^{2}(x^{2}-x-2)dx
limit as x approaches-5 of (x^2)/(5-x)	\lim\:_{x\to\:-5}(\frac{x^{2}}{5-x})
derivative of 9/(x^4)	\frac{d}{dx}(\frac{9}{x^{4}})
area 3x^2,-3x+6,-4,2	area\:3x^{2},-3x+6,-4,2
limit as x approaches 0+of (x+92)/x	\lim\:_{x\to\:0+}(\frac{x+92}{x})
integral of (e^x)/(sqrt(1+e^x))	\int\:\frac{e^{x}}{\sqrt{1+e^{x}}}dx
integral of x^9sqrt(x^5+3)	\int\:x^{9}\sqrt{x^{5}+3}dx
derivative of ln((5x^2))	\frac{d}{dx}(\ln((5x)^{2}))
y^{''}+7y^'=0	y^{\prime\:\prime\:}+7y^{\prime\:}=0
derivative of cot(3-2x)	\frac{d}{dx}(\cot(3-2x))
(d^2y)/(dt^2)+5(dy)/(dt)+6y=1	\frac{d^{2}y}{dt^{2}}+5\frac{dy}{dt}+6y=1
xy^2y^'=y^3-4x^3,y(1)=4	xy^{2}y^{\prime\:}=y^{3}-4x^{3},y(1)=4
inverse oflaplace ((-1/4))/(1+(1/2)*s)	inverselaplace\:\frac{(-\frac{1}{4})}{1+(\frac{1}{2})\cdot\:s}
derivative of (arctan(x)^2)	\frac{d}{dx}((\arctan(x))^{2})
limit as x approaches 1+of 1/(x+8)	\lim\:_{x\to\:1+}(\frac{1}{x+8})
(\partial)/(\partial x)(-6ysin(3x))	\frac{\partial\:}{\partial\:x}(-6y\sin(3x))
integral of 1/(xsqrt(4x^2+25))	\int\:\frac{1}{x\sqrt{4x^{2}+25}}dx
y=3cos(x)sin(x)	y=3\cos(x)\sin(x)
derivative of 8arcsin(e^{x/2})	derivative\:8\arcsin(e^{\frac{x}{2}})
inverse oflaplace s/(s^2(s^2+1))	inverselaplace\:\frac{s}{s^{2}(s^{2}+1)}
d/(dt)(e^{2t})	\frac{d}{dt}(e^{2t})
maclaurin (1-x)^{-1/2},4	maclaurin\:(1-x)^{-\frac{1}{2}},4
slope of y=x^2-3	slope\:y=x^{2}-3
f(x)=xsin(4/x)	f(x)=x\sin(\frac{4}{x})
derivative of 3x^2-e^{-x}	\frac{d}{dx}(3x^{2}-e^{-x})
area x=y^2,x=y^2+2	area\:x=y^{2},x=y^{2}+2
derivative of arcsin(cos(x^3))	derivative\:\arcsin(\cos(x^{3}))
tangent of f(x)=3x-2sqrt(x),\at x=1	tangent\:f(x)=3x-2\sqrt{x},\at\:x=1
(\partial)/(\partial y)((9y)/(x^5))	\frac{\partial\:}{\partial\:y}(\frac{9y}{x^{5}})
y^{''}+22y=0	y^{\prime\:\prime\:}+22y=0
(\partial)/(\partial y)(x^2+xy+y^2)	\frac{\partial\:}{\partial\:y}(x^{2}+xy+y^{2})
area 10-7x,y=0,x^2-20	area\:10-7x,y=0,x^{2}-20
integral of 2x+3x^{-2}	\int\:2x+3x^{-2}dx
integral of (5sin^3(sqrt(x)))/(sqrt(x))	\int\:\frac{5\sin^{3}(\sqrt{x})}{\sqrt{x}}dx
(dy)/(dt)+2y=3e^t,y(0)=1	\frac{dy}{dt}+2y=3e^{t},y(0)=1
integral of sqrt(4+5x^2)	\int\:\sqrt{4+5x^{2}}dx
integral of 1/(x*sqrt(x)+x^2)	\int\:\frac{1}{x\cdot\:\sqrt{x}+x^{2}}dx
integral from 0 to e of xln(x)	\int\:_{0}^{e}x\ln(x)dx
y^'=(x-2)(y-2)	y^{\prime\:}=(x-2)(y-2)
tangent of f(x)=-x+5x^{-1/2}-3,(1,1)	tangent\:f(x)=-x+5x^{-\frac{1}{2}}-3,(1,1)
(dy)/(dx)=((x-3))/(y-3)	\frac{dy}{dx}=\frac{(x-3)}{y-3}
integral from 0 to infinity of 1/(1+x)	\int\:_{0}^{\infty\:}\frac{1}{1+x}dx
integral of 2cos^2(θ)	\int\:2\cos^{2}(θ)dθ
derivative of (e^x+e^{-x}/(e^x-e^{-x)})	\frac{d}{dx}(\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}})
(d^3)/(dx^3)(x^2sin(sqrt(x)))	\frac{d^{3}}{dx^{3}}(x^{2}\sin(\sqrt{x}))
derivative of (a-x^2)	\frac{d}{dx}((a-x)^{2})
derivative of (x^5/(a+b)-(x^2)/(a-b))	\frac{d}{dx}(\frac{x^{5}}{a+b}-\frac{x^{2}}{a-b})
derivative of 1/(-2x^2)	\frac{d}{dx}(\frac{1}{-2x^{2}})
sum from n=0 to infinity of (2x)^n	\sum\:_{n=0}^{\infty\:}(2x)^{n}
tangent of f(x)=x2^x	tangent\:f(x)=x2^{x}
slope of (-2.3)(2.2)	slope\:(-2.3)(2.2)
limit as x approaches 0-of x*arctan(1/x)	\lim\:_{x\to\:0-}(x\cdot\:\arctan(\frac{1}{x}))
(dy)/(dx)=(2x)/(1+2y),y(2)=0	\frac{dy}{dx}=\frac{2x}{1+2y},y(2)=0
sum from n=1 to infinity}(-1)^{n-1 of (2^n)/(n^4)	\sum\:_{n=1}^{\infty\:}(-1)^{n-1}\frac{2^{n}}{n^{4}}
limit as x approaches 4 of 2^x	\lim\:_{x\to\:4}(2^{x})
(\partial)/(\partial x)(6x+5sqrt(y))	\frac{\partial\:}{\partial\:x}(6x+5\sqrt{y})
integral of (24t+6t^3)/(8t^2+t^4)	\int\:\frac{24t+6t^{3}}{8t^{2}+t^{4}}dt
derivative of sqrt(x/pi)	\frac{d}{dx}(\sqrt{\frac{x}{π}})
derivative of arccos(sqrt(y-2x))	\frac{d}{dx}(\arccos(\sqrt{y-2x}))
integral of sec^2(θ)tan^7(θ)	\int\:\sec^{2}(θ)\tan^{7}(θ)dθ
limit as x approaches 2 of (-1)/((x+2))	\lim\:_{x\to\:2}(\frac{-1}{(x+2)})
derivative of (2-x/(1+2x^2))	\frac{d}{dx}(\frac{2-x}{1+2x^{2}})
limit as x approaches 0 of sqrt(16-7x)	\lim\:_{x\to\:0}(\sqrt{16-7x})
integral of-cos(x)+C	\int\:-\cos(x)+Cdx
d/(dt)(4e^{-t})	\frac{d}{dt}(4e^{-t})
derivative of 4x^2-2	derivative\:4x^{2}-2
derivative of 3sqrt(4-1/2 x)	\frac{d}{dx}(3\sqrt{4-\frac{1}{2}x})
integral of x*sin(4x)	\int\:x\cdot\:\sin(4x)dx
derivative of (-2x/(x^2+1))	\frac{d}{dx}(\frac{-2x}{x^{2}+1})
integral of 12e^{3x-1}	\int\:12e^{3x-1}dx
integral of 6/((1-2x)^3)	\int\:\frac{6}{(1-2x)^{3}}dx
limit as x approaches 2 of sqrt(2x^2-4x)	\lim\:_{x\to\:2}(\sqrt{2x^{2}-4x})
integral of (3x^2)/(sqrt(1-6x^3))	\int\:\frac{3x^{2}}{\sqrt{1-6x^{3}}}dx
(\partial)/(\partial x)(ysin(z))	\frac{\partial\:}{\partial\:x}(y\sin(z))
limit as x approaches-8-of (x+2)/(x+8)	\lim\:_{x\to\:-8-}(\frac{x+2}{x+8})
area 8x-10,x^2-4x+10	area\:8x-10,x^{2}-4x+10
implicit (dy)/(dx),e^xy=1	implicit\:\frac{dy}{dx},e^{x}y=1
integral of x^2-2	\int\:x^{2}-2dx
d/(d{x)}(({y})/(sqrt({x)^2+{y)^2+{z}^2}})	\frac{d}{d{x}}(\frac{{y}}{\sqrt{{x}^{2}+{y}^{2}+{z}^{2}}})
(dy)/(dx)=(2y)/(3x)	\frac{dy}{dx}=\frac{2y}{3x}
tangent of f(x)=sqrt(5-3x),\at x=-2	tangent\:f(x)=\sqrt{5-3x},\at\:x=-2
limit as x approaches-5 of 4x^3+x	\lim\:_{x\to\:-5}(4x^{3}+x)
(dy)/(dx)+3y=2	\frac{dy}{dx}+3y=2
limit as x approaches 3 of-8	\lim\:_{x\to\:3}(-8)
integral of 1/((3+x)^2)	\int\:\frac{1}{(3+x)^{2}}dx
d/(dt)(ln(sqrt((a+bt)/(a-bt))))	\frac{d}{dt}(\ln(\sqrt{\frac{a+bt}{a-bt}}))
d/(ds)(2/(s^2+4))	\frac{d}{ds}(\frac{2}{s^{2}+4})
integral from 1 to 2 of x^2	\int\:_{1}^{2}x^{2}dx
integral from 0 to 2 of x/(sqrt(16-x^2))	\int\:_{0}^{2}\frac{x}{\sqrt{16-x^{2}}}dx
integral of 5/(2x+7)	\int\:\frac{5}{2x+7}dx
limit as x approaches 2 of (x+4)/(3x-1)	\lim\:_{x\to\:2}(\frac{x+4}{3x-1})
integral of 1/((4x^2-1)^2)	\int\:\frac{1}{(4x^{2}-1)^{2}}dx
integral of 2x(x^2+8)^7	\int\:2x(x^{2}+8)^{7}dx

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