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Popular Calculus Problems

tangent of f(x)=2x^2-10x+9,(2,-3)	tangent\:f(x)=2x^{2}-10x+9,(2,-3)
(x^2+y^2)dx+2xydy=0	(x^{2}+y^{2})dx+2xydy=0
sum from n=1 to infinity of (5n)/(n^2+2)	\sum\:_{n=1}^{\infty\:}\frac{5n}{n^{2}+2}
derivative of sqrt(x^3)-1/(x^7)	\frac{d}{dx}(\sqrt{x^{3}}-\frac{1}{x^{7}})
(dy)/(dx)-e^{x+y}=0	\frac{dy}{dx}-e^{x+y}=0
integral from 4 to 9 of (3sqrt(x))	\int\:_{4}^{9}(3\sqrt{x})dx
derivative of y=sqrt(x^2+2)	derivative\:y=\sqrt{x^{2}+2}
limit as x approaches infinity of (x^2)/(e^{x^3)}	\lim\:_{x\to\:\infty\:}(\frac{x^{2}}{e^{x^{3}}})
derivative of 17cos(x)	\frac{d}{dx}(17\cos(x))
limit as x approaches-2 of (x^2+5)/(x+2)	\lim\:_{x\to\:-2}(\frac{x^{2}+5}{x+2})
laplacetransform F(T)= 7/5	laplacetransform\:F(T)=\frac{7}{5}
derivative of x^3+(3-3x^2^2+4)	\frac{d}{dx}(x^{3}+(3-3x^{2})^{2}+4)
(dy)/(dx)+y=x^2-2	\frac{dy}{dx}+y=x^{2}-2
limit as x approaches 2 of sin((pix)/2)	\lim\:_{x\to\:2}(\sin(\frac{πx}{2}))
integral of 1/(u^{3/2)}	\int\:\frac{1}{u^{\frac{3}{2}}}du
derivative of 2sin^2(6x^4)	derivative\:2\sin^{2}(6x^{4})
derivative of (x-4/(x^2+1))	\frac{d}{dx}(\frac{x-4}{x^{2}+1})
derivative of In(3x)	\frac{d}{dx}(In(3x))
(\partial)/(\partial y)(x^{0.5}y^{0.5})	\frac{\partial\:}{\partial\:y}(x^{0.5}y^{0.5})
derivative of cos(3x^2-2x)	\frac{d}{dx}(\cos(3x^{2}-2x))
integral of (x^3)/(sqrt(5x^4-1))	\int\:\frac{x^{3}}{\sqrt{5x^{4}-1}}dx
integral of (3x+4)^3	\int\:(3x+4)^{3}dx
derivative of 1/(sqrt(x^2-1))	derivative\:\frac{1}{\sqrt{x^{2}-1}}
derivative of 1+1/(sqrt(x))	\frac{d}{dx}(1+\frac{1}{\sqrt{x}})
xy^'=y+8x^2sin(x),y(pi)=0	xy^{\prime\:}=y+8x^{2}\sin(x),y(π)=0
x^2(dy)/(dx)+2xy-y^3=0	x^{2}\frac{dy}{dx}+2xy-y^{3}=0
derivative of (sqrt(10)/(x^7))	\frac{d}{dx}(\frac{\sqrt{10}}{x^{7}})
limit as x approaches 0-of 1/(3x)	\lim\:_{x\to\:0-}(\frac{1}{3x})
area y=sqrt(3x),x=3,y=1	area\:y=\sqrt{3x},x=3,y=1
y^'+y=xy^2	y^{\prime\:}+y=xy^{2}
limit as x approaches infinity of 2x^2+5	\lim\:_{x\to\:\infty\:}(2x^{2}+5)
integral of (x^2-x+2)/(x^3-x^2+x-1)	\int\:\frac{x^{2}-x+2}{x^{3}-x^{2}+x-1}dx
(\partial)/(\partial x)(cos(z)+xy^2)	\frac{\partial\:}{\partial\:x}(\cos(z)+xy^{2})
tangent of f(x)= 1/(4x^{3/2)},\at x=4	tangent\:f(x)=\frac{1}{4x^{\frac{3}{2}}},\at\:x=4
(dy)/(dx)=6x^2y	\frac{dy}{dx}=6x^{2}y
sum from n=1 to infinity of ne^{-8n}	\sum\:_{n=1}^{\infty\:}ne^{-8n}
integral of 1/(x^2)ln(x)	\int\:\frac{1}{x^{2}}\ln(x)dx
d/(dy)((ln(y))/(2sqrt(y))+1/(sqrt(y)))	\frac{d}{dy}(\frac{\ln(y)}{2\sqrt{y}}+\frac{1}{\sqrt{y}})
limit as x approaches-2 of-10	\lim\:_{x\to\:-2}(-10)
xy^'+y=y^2,y(1)=-9	xy^{\prime\:}+y=y^{2},y(1)=-9
derivative of cosh(3x)	\frac{d}{dx}(\cosh(3x))
integral of rsin(r^2)	\int\:r\sin(r^{2})dr
integral of (2x^2+6)/((x^2-2x+2)^2)	\int\:\frac{2x^{2}+6}{(x^{2}-2x+2)^{2}}dx
limit as x approaches infinity of ln(2x)	\lim\:_{x\to\:\infty\:}(\ln(2x))
area x=-1,x=3,y=x^3-1,y=0	area\:x=-1,x=3,y=x^{3}-1,y=0
derivative of x^8ln(5x)	\frac{d}{dx}(x^{8}\ln(5x))
derivative of 1200sqrt(x^2-0.2x)	\frac{d}{dx}(1200\sqrt{x^{2}-0.2x})
derivative of x^3-12x-5	\frac{d}{dx}(x^{3}-12x-5)
derivative of 2-4x	\frac{d}{dx}(2-4x)
integral of 1/(sqrt(4x^2+2))	\int\:\frac{1}{\sqrt{4x^{2}+2}}dx
integral from 0 to pi of t^2e^{-st}	\int\:_{0}^{π}t^{2}e^{-st}dt
area y=e^x,y=e^{-x},x=1	area\:y=e^{x},y=e^{-x},x=1
derivative of xe^{-5x}	derivative\:xe^{-5x}
y^'=(6x^2+y^2)/(xy)	y^{\prime\:}=\frac{6x^{2}+y^{2}}{xy}
integral of ye^{xy}	\int\:ye^{xy}dx
integral of xsqrt(5x+1)	\int\:x\sqrt{5x+1}dx
limit as x approaches 2+of 2x-[\|x\|]	\lim\:_{x\to\:2+}(2x-[\left\|x\right\|])
derivative of 4/((x+4^2))	\frac{d}{dx}(\frac{4}{(x+4)^{2}})
t*(dy)/(dt)=t^3+22t^3y	t\cdot\:\frac{dy}{dt}=t^{3}+22t^{3}y
integral of 1/(4x-x^2)	\int\:\frac{1}{4x-x^{2}}dx
derivative of arctan(2x+1)	\frac{d}{dx}(\arctan(2x+1))
derivative of x^2-4x+9	\frac{d}{dx}(x^{2}-4x+9)
y^{''}+4y^'+4y=e^{-2x}+x^2	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{-2x}+x^{2}
(dy)/(dx)=13x^{12}y	\frac{dy}{dx}=13x^{12}y
derivative of arcsin((x-2/1))	\frac{d}{dx}(\arcsin(\frac{x-2}{1}))
integral from 2 to 6 of pi(y-2)2	\int\:_{2}^{6}π(y-2)2dy
(dy)/(dx)=(cos(5x))/(e^{5y)}	\frac{dy}{dx}=\frac{\cos(5x)}{e^{5y}}
derivative of x/(2x-1)	\frac{d}{dx}(\frac{x}{2x-1})
(dy)/(dt)=-4y	\frac{dy}{dt}=-4y
integral of 100x	\int\:100xdx
derivative of 4pir^2	derivative\:4πr^{2}
derivative of tan(6x+x^{-4})	\frac{d}{dx}(\tan(6x)+x^{-4})
integral of cos(x)*e^{sin(x)}	\int\:\cos(x)\cdot\:e^{\sin(x)}dx
derivative of x-1/3 x^3	\frac{d}{dx}(x-\frac{1}{3}x^{3})
integral of x/(sqrt(x+10))	\int\:\frac{x}{\sqrt{x+10}}dx
integral of sec(x)(tan(x)+cos(x))	\int\:\sec(x)(\tan(x)+\cos(x))dx
derivative of (4x^{ln(4x)})	\frac{d}{dx}((4x)^{\ln(4x)})
limit as x approaches 6 of 4/(x-6)	\lim\:_{x\to\:6}(\frac{4}{x-6})
taylor 9ln(5-8x^2)	taylor\:9\ln(5-8x^{2})
integral of 3tcos(2t)	\int\:3t\cos(2t)dt
limit as x approaches 8 of (\|8-x\|)/(8-x)	\lim\:_{x\to\:8}(\frac{\left\|8-x\right\|}{8-x})
limit as x approaches 3-of (7-x)/(x-3)	\lim\:_{x\to\:3-}(\frac{7-x}{x-3})
integral of sqrt(1-4x)	\int\:\sqrt{1-4x}dx
integral of 3x^2(x-2)(x+3)	\int\:3x^{2}(x-2)(x+3)dx
integral from 1 to 2 of 3(ln(x))/(x^2)	\int\:_{1}^{2}3\frac{\ln(x)}{x^{2}}dx
derivative of sqrt(x)dx	\frac{d}{dx}(\sqrt{x}dx)
derivative of (1+x^{-3})	\frac{d}{dx}((1+x)^{-3})
integral of (t+1/t)^{3/2}((t^2-1)/(t^2))	\int\:(t+\frac{1}{t})^{\frac{3}{2}}(\frac{t^{2}-1}{t^{2}})dt
integral of 1/(sqrt(e^{2y)-1)}	\int\:\frac{1}{\sqrt{e^{2y}-1}}dy
integral from 0 to pi/4 of x^2sin(2x)	\int\:_{0}^{\frac{π}{4}}x^{2}\sin(2x)dx
derivative of 1/(4x^2+3x)	derivative\:\frac{1}{4x^{2}+3x}
integral of 36e^{4x}sqrt(3+e^{4x)}	\int\:36e^{4x}\sqrt{3+e^{4x}}dx
limit as x approaches 1 of (2-7x)/(x+6)	\lim\:_{x\to\:1}(\frac{2-7x}{x+6})
limit as x approaches 0 of (1+x^2)-1	\lim\:_{x\to\:0}((1+x^{2})-1)
(\partial)/(\partial z)((e^{xz+y})/(z^2+w))	\frac{\partial\:}{\partial\:z}(\frac{e^{xz+y}}{z^{2}+w})
integral of sqrt(25-x^2)(2x)	\int\:\sqrt{25-x^{2}}(2x)dx
integral from 2 to 5 of e^{4x}	\int\:_{2}^{5}e^{4x}dx
integral of t/(sqrt(9+t^2))	\int\:\frac{t}{\sqrt{9+t^{2}}}dt
integral of (1-1/x)^2	\int\:(1-\frac{1}{x})^{2}dx
derivative of sin((pix/8))	\frac{d}{dx}(\sin(\frac{πx}{8}))

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