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Popular Calculus Problems

limit as x approaches 0 of 500	\lim\:_{x\to\:0}(500)
(\partial)/(\partial x)((4x^3y^4+9)^2)	\frac{\partial\:}{\partial\:x}((4x^{3}y^{4}+9)^{2})
integral from-3 to 5 of \|x\|	\int\:_{-3}^{5}\left\|x\right\|dx
(\partial)/(\partial x)(x^3y+y^2)	\frac{\partial\:}{\partial\:x}(x^{3}y+y^{2})
inverse oflaplace 1/((s+2))	inverselaplace\:\frac{1}{(s+2)}
derivative of cos(arctan(4x))	derivative\:\cos(\arctan(4x))
integral from 0 to 1 of 2pi(2-y)(2-2y^2)	\int\:_{0}^{1}2π(2-y)(2-2y^{2})dy
sum from n=1 to infinity of 15^nx^nn!	\sum\:_{n=1}^{\infty\:}15^{n}x^{n}n!
integral of 1/(x^2sqrt(x^2+64))	\int\:\frac{1}{x^{2}\sqrt{x^{2}+64}}dx
(-sin^3(x)+2cos^2(x)sin(x))^'	(-\sin^{3}(x)+2\cos^{2}(x)\sin(x))^{\prime\:}
derivative of f(x)= 7/4 x^2-3x+12	derivative\:f(x)=\frac{7}{4}x^{2}-3x+12
derivative of 5sin(10x)	\frac{d}{dx}(5\sin(10x))
tangent of f(x)=x+sqrt(x),\at x=25	tangent\:f(x)=x+\sqrt{x},\at\:x=25
derivative of y=x^{-9}	derivative\:y=x^{-9}
derivative of 10sin^3(x)	\frac{d}{dx}(10\sin^{3}(x))
(\partial)/(\partial x)(y^3cos(3x))	\frac{\partial\:}{\partial\:x}(y^{3}\cos(3x))
area e^{3x}+1,y=0,x=0,x=0.6	area\:e^{3x}+1,y=0,x=0,x=0.6
y^{''}+14y^'+49y=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}+14y^{\prime\:}+49y=0,y(0)=0,y^{\prime\:}(0)=1
(\partial)/(\partial x)((2x+2y)^{1/2})	\frac{\partial\:}{\partial\:x}((2x+2y)^{\frac{1}{2}})
integral of (3^x)/(ln(3))	\int\:\frac{3^{x}}{\ln(3)}dx
derivative of sin(2x^3)	\frac{d}{dx}(\sin(2x^{3}))
6xy^'-2y=((-x^2))/(y^5)	6xy^{\prime\:}-2y=\frac{(-x^{2})}{y^{5}}
derivative of (cot(x)/x)	\frac{d}{dx}(\frac{\cot(x)}{x})
derivative of (3+xf(x))/(sqrt(x))	derivative\:\frac{3+xf(x)}{\sqrt{x}}
derivative of ln(1-(10/x))	\frac{d}{dx}(\ln(1-\frac{10}{x}))
integral of-cos(x)sin(x)	\int\:-\cos(x)\sin(x)dx
derivative of f(x)=sqrt(5x+1)	derivative\:f(x)=\sqrt{5x+1}
integral from 1/7 to 5 of 4xln(7x)	\int\:_{\frac{1}{7}}^{5}4x\ln(7x)dx
derivative of f(x)= 9/(x^2+5)	derivative\:f(x)=\frac{9}{x^{2}+5}
derivative of f(x)=((tan(x)-1))/(sec(x))	derivative\:f(x)=\frac{(\tan(x)-1)}{\sec(x)}
integral from 0 to 3 of 1/(2x+3)	\int\:_{0}^{3}\frac{1}{2x+3}dx
derivative of x-ln(xe^x)	\frac{d}{dx}(x-\ln(xe^{x}))
derivative of 2-2/x	\frac{d}{dx}(2-\frac{2}{x})
integral of 1/(x^{2/5)}	\int\:\frac{1}{x^{\frac{2}{5}}}dx
integral from 0 to 2 of x^2	\int\:_{0}^{2}x^{2}dx
integral of e^{x^2}x^2	\int\:e^{x^{2}}x^{2}dx
y^'=e^{5y+8x},y(0)=3	y^{\prime\:}=e^{5y+8x},y(0)=3
derivative of 2/(e^x+e^{-x})	\frac{d}{dx}(\frac{2}{e^{x}+e^{-x}})
derivative of (2x^4+3x^2-1/(x^2))	\frac{d}{dx}(\frac{2x^{4}+3x^{2}-1}{x^{2}})
limit as x approaches pi/2 of pi/2-x	\lim\:_{x\to\:\frac{π}{2}}(\frac{π}{2}-x)
derivative of 2/(7x^2)	derivative\:\frac{2}{7x^{2}}
integral of ((x^2+2x+3))/((x^3+3x^2+9x))	\int\:\frac{(x^{2}+2x+3)}{(x^{3}+3x^{2}+9x)}dx
d/(dy)(3xy)	\frac{d}{dy}(3xy)
limit as x approaches 0 of (1-3x)^{3/x}	\lim\:_{x\to\:0}((1-3x)^{\frac{3}{x}})
integral from 0 to 2pi of sin^2(4x)	\int\:_{0}^{2π}\sin^{2}(4x)dx
tangent of y= 6/(sqrt(x)),(4, 6/2)	tangent\:y=\frac{6}{\sqrt{x}},(4,\frac{6}{2})
integral of (e^x)/3	\int\:\frac{e^{x}}{3}dx
integral of (6-e^x)/(e^{5x)}	\int\:\frac{6-e^{x}}{e^{5x}}dx
area e^x,e^{-4x},0,ln(4)	area\:e^{x},e^{-4x},0,\ln(4)
f(x)=3x^5	f(x)=3x^{5}
derivative of e^{-x}-1	\frac{d}{dx}(e^{-x}-1)
integral of 5xsin(x^2)	\int\:5x\sin(x^{2})dx
integral of cos(3xy)	\int\:\cos(3xy)dx
limit as x approaches 0+of x(2)	\lim\:_{x\to\:0+}(x(2))
limit as x approaches 0 of e^xcos(3x)	\lim\:_{x\to\:0}(e^{x}\cos(3x))
integral of 1/(e^{2x)-3e^x}	\int\:\frac{1}{e^{2x}-3e^{x}}dx
d/(dt)(tan(3t))	\frac{d}{dt}(\tan(3t))
(\partial)/(\partial x)((3x^2)/(5-x))	\frac{\partial\:}{\partial\:x}(\frac{3x^{2}}{5-x})
integral of 1/((1+9x^2))	\int\:\frac{1}{(1+9x^{2})}dx
derivative of 9*sqrt(t+1)	derivative\:9\cdot\:\sqrt{t+1}
derivative of xe^{-x/4}	\frac{d}{dx}(xe^{-\frac{x}{4}})
derivative of y/(y-x)	\frac{d}{dx}(\frac{y}{y-x})
derivative of e^{5x+1}arccsch(sqrt(x+1))	\frac{d}{dx}(e^{5x+1}\arccsch(\sqrt{x+1}))
sum from n=1 to infinity of 2/(3^{2n)}	\sum\:_{n=1}^{\infty\:}\frac{2}{3^{2n}}
derivative of (11/(sqrt(x)))	\frac{d}{dx}(\frac{11}{\sqrt{x}})
derivative of x-\sqrt[3]{x}	derivative\:x-\sqrt[3]{x}
integral of (x^2)/(sqrt(x^2+3))	\int\:\frac{x^{2}}{\sqrt{x^{2}+3}}dx
y^{'''}+4y^'=sec(2x)	y^{\prime\:\prime\:\prime\:}+4y^{\prime\:}=\sec(2x)
(dy)/(dx)=3y(5-y)	\frac{dy}{dx}=3y(5-y)
limit as x approaches 0 of 3pi	\lim\:_{x\to\:0}(3π)
limit as x approaches 0 of ((7^x-1))/x	\lim\:_{x\to\:0}(\frac{(7^{x}-1)}{x})
taylor x-sin(x)	taylor\:x-\sin(x)
f(θ)=4cos(θ)	f(θ)=4\cos(θ)
integral of 4xe^{2/3 x}	\int\:4xe^{\frac{2}{3}x}dx
limit as x approaches-16 of sqrt(x+16)-4	\lim\:_{x\to\:-16}(\sqrt{x+16}-4)
y^{''}-3y^'-18y=0,y(0)=1,y^'(0)=-2	y^{\prime\:\prime\:}-3y^{\prime\:}-18y=0,y(0)=1,y^{\prime\:}(0)=-2
derivative of x/((x^2+1^{1/2)})	\frac{d}{dx}(\frac{x}{(x^{2}+1)^{\frac{1}{2}}})
(d^2)/(dx^2)((2x^2+7)^5)	\frac{d^{2}}{dx^{2}}((2x^{2}+7)^{5})
derivative of In,x^2	\frac{d}{dx}(In,x^{2})
integral of 3/(x^2)	\int\:\frac{3}{x^{2}}dx
derivative of 2(x^3-1^5)	\frac{d}{dx}(2(x^{3}-1)^{5})
2x^2y^{''}+xy^'+y=0	2x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}+y=0
derivative of f(x)=-16t^2+145	derivative\:f(x)=-16t^{2}+145
(dP)/(dt)=kP	\frac{dP}{dt}=kP
slope of (3,3),(0,-6)	slope\:(3,3),(0,-6)
f(x)=4tan(x)	f(x)=4\tan(x)
sum from n=0 to infinity of \sqrt[n]{2}	\sum\:_{n=0}^{\infty\:}\sqrt[n]{2}
integral from 2 to infinity of x/(x^2+1)	\int\:_{2}^{\infty\:}\frac{x}{x^{2}+1}dx
derivative of x^2+4x+1	derivative\:x^{2}+4x+1
integral of 2xsqrt(6x-x^2)	\int\:2x\sqrt{6x-x^{2}}dx
integral of ((4-ln(x+3))^3)/(x+3)	\int\:\frac{(4-\ln(x+3))^{3}}{x+3}dx
derivative of sqrt(1-(x^2/(y^2)))	\frac{d}{dx}(\sqrt{1-\frac{x^{2}}{y^{2}}})
taylor (1+x)^k,0	taylor\:(1+x)^{k},0
integral of 1.830496064e^{2.1342x}sin(x)	\int\:1.830496064e^{2.1342x}\sin(x)dx
integral of 4cos(sqrt(2x))	\int\:4\cos(\sqrt{2x})dx
(\partial)/(\partial y)(xsqrt(y^2+1))	\frac{\partial\:}{\partial\:y}(x\sqrt{y^{2}+1})
y^{''}-4sqrt(3)y^'+12y=0	y^{\prime\:\prime\:}-4\sqrt{3}y^{\prime\:}+12y=0
derivative of 1/3 ln(e^x+1)	\frac{d}{dx}(\frac{1}{3}\ln(e^{x}+1))
derivative of-(2x/(1-x^2))	\frac{d}{dx}(-\frac{2x}{1-x^{2}})
f(x)=-x^2sin(x)+4xcos(x)+2sin(x)	f(x)=-x^{2}\sin(x)+4x\cos(x)+2\sin(x)

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