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Popular Calculus Problems

area y=x^2-15,y=1	area\:y=x^{2}-15,y=1
limit as (x,y) approaches (0,1) of (e^{xy})/(x+1)	\lim\:_{(x,y)\to\:(0,1)}(\frac{e^{xy}}{x+1})
integral of cos(y^3)	\int\:\cos(y^{3})dy
tangent of f(x)=(x^3),\at x=2	tangent\:f(x)=(x^{3}),\at\:x=2
limit as x approaches 2 of (2-x)/(\|x-2\|)	\lim\:_{x\to\:2}(\frac{2-x}{\left\|x-2\right\|})
(dy)/(dt)-2ty=-6t^2e^{t^2}	\frac{dy}{dt}-2ty=-6t^{2}e^{t^{2}}
integral of (cos^3(x))	\int\:(\cos^{3}(x))dx
limit as x approaches 3 of 5x+2	\lim\:_{x\to\:3}(5x+2)
limit as x approaches 4 of sqrt(32-x^2)	\lim\:_{x\to\:4}(\sqrt{32-x^{2}})
(dy)/(dx)=(2xy)/(1+x^2)	\frac{dy}{dx}=\frac{2xy}{1+x^{2}}
tangent of g(x)=7sqrt(x),\at x=9	tangent\:g(x)=7\sqrt{x},\at\:x=9
(dy)/(dt)=1600-(4y)/(170)	\frac{dy}{dt}=1600-\frac{4y}{170}
(\partial)/(\partial x)((x^2y-1)/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}y-1}{x^{2}})
derivative of sqrt(21x)	\frac{d}{dx}(\sqrt{21x})
(\partial)/(\partial x)(sqrt(20-x^2-7y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{20-x^{2}-7y^{2}})
derivative of ln((1+e^x/(1-e^x)))	\frac{d}{dx}(\ln(\frac{1+e^{x}}{1-e^{x}}))
integral of (x-1)^3	\int\:(x-1)^{3}dx
integral of 1/((x+1)^3)	\int\:\frac{1}{(x+1)^{3}}dx
limit as x approaches 2 of sqrt(4-x^2)	\lim\:_{x\to\:2}(\sqrt{4-x^{2}})
limit as x approaches 2 of 5x^4	\lim\:_{x\to\:2}(5x^{4})
limit as x approaches 2 of (x-2)/(x+2)	\lim\:_{x\to\:2}(\frac{x-2}{x+2})
integral of sin(3pix)	\int\:\sin(3πx)dx
sum from n=0 to infinity of 8^n	\sum\:_{n=0}^{\infty\:}8^{n}
derivative of 2/((5x+1^3))	\frac{d}{dx}(\frac{2}{(5x+1)^{3}})
integral of 96-32t	\int\:96-32tdt
derivative of \sqrt[5]{(x^3-2/(x^3+2)})	\frac{d}{dx}(\sqrt[5]{\frac{x^{3}-2}{x^{3}+2}})
y^'=xe^6	y^{\prime\:}=xe^{6}
integral of ((x^2+1)(x^4-x^2+1))/(2x^3)	\int\:\frac{(x^{2}+1)(x^{4}-x^{2}+1)}{2x^{3}}dx
derivative of (1+9x^2)(x+x^2)	derivative\:(1+9x^{2})(x+x^{2})
integral of 2/(4-9x^2)	\int\:\frac{2}{4-9x^{2}}dx
limit as x approaches-4 of 6-3x	\lim\:_{x\to\:-4}(6-3x)
derivative of y=x^22^{x^2}	derivative\:y=x^{2}2^{x^{2}}
(x+3t)(dx)/(dt)+3x-t=0	(x+3t)\frac{dx}{dt}+3x-t=0
(dy}{dx}+\frac{7y)/x =-5x-10	\frac{dy}{dx}+\frac{7y}{x}=-5x-10
(\partial)/(\partial x)(9x^7y^6+7x^5y^8)	\frac{\partial\:}{\partial\:x}(9x^{7}y^{6}+7x^{5}y^{8})
derivative of (3x-4)^2	derivative\:(3x-4)^{2}
derivative of f(x)= 5/(1+x^2)	derivative\:f(x)=\frac{5}{1+x^{2}}
sum from n=1 to infinity of ne^{-4n}	\sum\:_{n=1}^{\infty\:}ne^{-4n}
tangent of y=x^4+9x^2-x	tangent\:y=x^{4}+9x^{2}-x
integral of 1/2 sec^2(5x)	\int\:\frac{1}{2}\sec^{2}(5x)dx
integral of (3x\sqrt[3]{x^2+2}+e^{5x})	\int\:(3x\sqrt[3]{x^{2}+2}+e^{5x})dx
derivative of sqrt(x)+2/(sqrt(x))	derivative\:\sqrt{x}+\frac{2}{\sqrt{x}}
slope of 36=9x^2-4y^2	slope\:36=9x^{2}-4y^{2}
integral of t^2e^{-st}	\int\:t^{2}e^{-st}dt
integral of (sin(x))/(3+cos^2(x))	\int\:\frac{\sin(x)}{3+\cos^{2}(x)}dx
derivative of ln(3x+1)	derivative\:\ln(3x+1)
limit as x approaches 0+of sin(1/x)	\lim\:_{x\to\:0+}(\sin(\frac{1}{x}))
integral from 0 to 4 of 6x+1/((x+3)^2)	\int\:_{0}^{4}6x+\frac{1}{(x+3)^{2}}dx
derivative of-x^3+9x^2-24x+5	\frac{d}{dx}(-x^{3}+9x^{2}-24x+5)
(\partial)/(\partial x)(3x^2-2xy-4y^2)	\frac{\partial\:}{\partial\:x}(3x^{2}-2xy-4y^{2})
(dy)/(dt)*1/4+y=cos(t)	\frac{dy}{dt}\cdot\:\frac{1}{4}+y=\cos(t)
integral of-1/3 e^{-3t}	\int\:-\frac{1}{3}e^{-3t}dt
derivative of 3x+e^x	\frac{d}{dx}(3x+e^{x})
(\partial)/(\partial y)(sqrt(4-x^2-7y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{4-x^{2}-7y^{2}})
2y^{''}+3y^'+y=t^2+2sin(t)	2y^{\prime\:\prime\:}+3y^{\prime\:}+y=t^{2}+2\sin(t)
derivative of arcsin(2/x)	\frac{d}{dx}(\arcsin(\frac{2}{x}))
(x^2+y+y^2)dx-xdy=0	(x^{2}+y+y^{2})dx-xdy=0
integral of 7/(x^2+3x-10)	\int\:\frac{7}{x^{2}+3x-10}dx
sum from n=2 to infinity of 1/(sqrt(n))	\sum\:_{n=2}^{\infty\:}\frac{1}{\sqrt{n}}
integral from 0 to infinity of 8/(x^2+1)	\int\:_{0}^{\infty\:}\frac{8}{x^{2}+1}dx
derivative of sec^2(4x)	derivative\:\sec^{2}(4x)
(\partial)/(\partial x)(x^{8/x})	\frac{\partial\:}{\partial\:x}(x^{\frac{8}{x}})
integral of (12x^3-1)/(3x^4-x+10)	\int\:\frac{12x^{3}-1}{3x^{4}-x+10}dx
integral of ((e^x+e^{-x}))/(e^x-e^{-x)}	\int\:\frac{(e^{x}+e^{-x})}{e^{x}-e^{-x}}dx
integral of ((x-1)^2)/(x^2)	\int\:\frac{(x-1)^{2}}{x^{2}}dx
area 3cos(8x),3-3cos(8x),[0, pi/8 ]	area\:3\cos(8x),3-3\cos(8x),[0,\frac{π}{8}]
derivative of 4/3 x^3-4x+3	\frac{d}{dx}(\frac{4}{3}x^{3}-4x+3)
f(x)= 1/(x-4)	f(x)=\frac{1}{x-4}
integral from 0 to pi/3 of sin(x)ln(cos(x))	\int\:_{0}^{\frac{π}{3}}\sin(x)\ln(\cos(x))dx
integral of cos^2(ln(x))	\int\:\cos^{2}(\ln(x))dx
(\partial)/(\partial x)(y+(1/(1/x+1/z)))	\frac{\partial\:}{\partial\:x}(y+(\frac{1}{\frac{1}{x}+\frac{1}{z}}))
integral of x/(sqrt(1+x^2)+x)	\int\:\frac{x}{\sqrt{1+x^{2}}+x}dx
limit as n approaches infinity of \|n\|	\lim\:_{n\to\:\infty\:}(\left\|n\right\|)
integral of e^{4/x}	\int\:e^{\frac{4}{x}}dx
derivative of ln(2x-x^2)	derivative\:\ln(2x-x^{2})
area y=x,y= 1/(x^2),x=2	area\:y=x,y=\frac{1}{x^{2}},x=2
y^'+(2y)/x =-4/x ,y(1)=3	y^{\prime\:}+\frac{2y}{x}=-\frac{4}{x},y(1)=3
(1/(e^x))^'	(\frac{1}{e^{x}})^{\prime\:}
derivative of x+sqrt(x)+8	\frac{d}{dx}(x+\sqrt{x}+8)
(5x+ye^{y/x})dx-xe^{y/x}dy=0	(5x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0
y^'= y/x+((2x^3)/y)cos(x^2)	y^{\prime\:}=\frac{y}{x}+(\frac{2x^{3}}{y})\cos(x^{2})
limit as x approaches 0 of (2x-1)^3	\lim\:_{x\to\:0}((2x-1)^{3})
limit as x approaches 9-of (-3)/((x-9)^2)	\lim\:_{x\to\:9-}(\frac{-3}{(x-9)^{2}})
integral from-1 to 1 of 1-y^2-(y^2-1)	\int\:_{-1}^{1}1-y^{2}-(y^{2}-1)dy
slope ofintercept (3,-2),(4,-7)	slopeintercept\:(3,-2),(4,-7)
(\partial)/(\partial x)(-3xe^{-2xy})	\frac{\partial\:}{\partial\:x}(-3xe^{-2xy})
derivative of sqrt(3x^2-5x)	\frac{d}{dx}(\sqrt{3x^{2}-5x})
limit as x approaches 1+of (x-2)^2	\lim\:_{x\to\:1+}((x-2)^{2})
y^{''}+9y=30sin(3t)	y^{\prime\:\prime\:}+9y=30\sin(3t)
2xy^2+2x+(x^2y+4y)y^'=0	2\cdot\:x\cdot\:y^{2}+2\cdot\:x+(x^{2}\cdot\:y+4\cdot\:y)\cdot\:y^{\prime\:}=0
d/(dy)(x^2+xy)	\frac{d}{dy}(x^{2}+xy)
derivative of 7x^6e^x+e^xx^7	derivative\:7x^{6}e^{x}+e^{x}x^{7}
integral of cos(3x+5)	\int\:\cos(3x+5)dx
d/(dt)(2t)	\frac{d}{dt}(2t)
(\partial)/(\partial x)(sin(x)cos(iy))	\frac{\partial\:}{\partial\:x}(\sin(x)\cos(iy))
integral of xsin(1/x)	\int\:x\sin(\frac{1}{x})dx
integral of 2/(sqrt(2x))	\int\:\frac{2}{\sqrt{2x}}dx
d/(dt)(sqrt(2)cos(t)-sqrt(2))	\frac{d}{dt}(\sqrt{2}\cos(t)-\sqrt{2})
integral of 1/(1+x+x^2)	\int\:\frac{1}{1+x+x^{2}}dx
integral of y^{-3}	\int\:y^{-3}dy

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