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Popular Calculus Problems

derivative of xe^{-x}-e^{-x}	\frac{d}{dx}(xe^{-x}-e^{-x})
sum from n=1 to infinity of n3^{-n}	\sum\:_{n=1}^{\infty\:}n3^{-n}
limit as x approaches 0 of 1/(3x)	\lim\:_{x\to\:0}(\frac{1}{3x})
xy^'-y=xln(x)	xy^{\prime\:}-y=x\ln(x)
derivative of 4^xx^4	derivative\:4^{x}x^{4}
x(x+1)((dy)/(dx))+xy=1	x(x+1)(\frac{dy}{dx})+xy=1
(x^2+y^2)dx+6xydy=0	(x^{2}+y^{2})dx+6xydy=0
inverse oflaplace 1/((s^2+4)(s^2-4))	inverselaplace\:\frac{1}{(s^{2}+4)(s^{2}-4)}
integral of 1/((x-5))	\int\:\frac{1}{(x-5)}dx
derivative of x+2y	\frac{d}{dx}(x+2y)
integral of (x^3)/(\sqrt[9]{x^2+9)}	\int\:\frac{x^{3}}{\sqrt[9]{x^{2}+9}}dx
y^'=y(3-ty),y(0)=1	y^{\prime\:}=y(3-ty),y(0)=1
(\partial)/(\partial x)(3cos(x+y))	\frac{\partial\:}{\partial\:x}(3\cos(x+y))
limit as x approaches-100 of 3x^2	\lim\:_{x\to\:-100}(3x^{2})
derivative of 2x^2-3x	\frac{d}{dx}(2x^{2}-3x)
limit as x approaches 7 of 1/((x-7)^2)	\lim\:_{x\to\:7}(\frac{1}{(x-7)^{2}})
d/(dy)(1/y e^{xy}-ln(y^2))	\frac{d}{dy}(\frac{1}{y}e^{xy}-\ln(y^{2}))
limit as x approaches-infinity of 2x-3	\lim\:_{x\to\:-\infty\:}(2x-3)
integral of 3x^2+y^2	\int\:3x^{2}+y^{2}dx
limit as x approaches 6 of 1/x	\lim\:_{x\to\:6}(\frac{1}{x})
(dx)/(dt)=x^{1/2}	\frac{dx}{dt}=x^{\frac{1}{2}}
simplify f(5)	simplify\:f(5)
area 5cos(x),5cos(2x),[0,pi]	area\:5\cos(x),5\cos(2x),[0,π]
integral of (cos^5(3x))/(sin^{14)(3x)}	\int\:\frac{\cos^{5}(3x)}{\sin^{14}(3x)}dx
derivative of (x-1)/(x^2)	derivative\:\frac{x-1}{x^{2}}
derivative of sin(t/(sqrt(t+4)))	derivative\:\sin(\frac{t}{\sqrt{t+4}})
derivative of x^4-4x^3	derivative\:x^{4}-4x^{3}
limit as x approaches 0+of tan(1/x)	\lim\:_{x\to\:0+}(\tan(\frac{1}{x}))
(\partial)/(\partial y)(ln(sqrt(xy)))	\frac{\partial\:}{\partial\:y}(\ln(\sqrt{xy}))
integral of (3y^2-2sin(y))	\int\:(3y^{2}-2\sin(y))dy
expand (x-2)^2(x-3)^3	expand\:(x-2)^{2}(x-3)^{3}
integral from 0 to infinity of x/(x^3)	\int\:_{0}^{\infty\:}\frac{x}{x^{3}}dx
expand (5x^6+2x^3)^4	expand\:(5x^{6}+2x^{3})^{4}
parity f(x)=xe^xcsc(x)	parity\:f(x)=xe^{x}\csc(x)
integral of 9e^{x/4}	\int\:9e^{\frac{x}{4}}dx
integral from-infinity to 0 of xe^{-x}	\int\:_{-\infty\:}^{0}xe^{-x}dx
tangent of y=sqrt(5x),(5,5)	tangent\:y=\sqrt{5x},(5,5)
integral of 3x^2e^{2x^3}	\int\:3x^{2}e^{2x^{3}}dx
derivative of x-x^2	derivative\:x-x^{2}
(4t)^'	(4t)^{\prime\:}
y=(xsin(x))/(1+x)	y=\frac{x\sin(x)}{1+x}
derivative of 3e^{-5x}ln(x)	\frac{d}{dx}(3e^{-5x}\ln(x))
derivative of ln(sin(8x))	derivative\:\ln(\sin(8x))
(d^2)/(dx^2)(ax^2+bx+c)	\frac{d^{2}}{dx^{2}}(ax^{2}+bx+c)
limit as x approaches infinity of 0.4^x	\lim\:_{x\to\:\infty\:}(0.4^{x})
d/(da)(tan(a)csc(a))	\frac{d}{da}(\tan(a)\csc(a))
derivative of g(t)=sqrt(1+ln(t))	derivative\:g(t)=\sqrt{1+\ln(t)}
tangent of f(x)=x^3,\at x=4	tangent\:f(x)=x^{3},\at\:x=4
(\partial)/(\partial x)((yx)/(1+yx))	\frac{\partial\:}{\partial\:x}(\frac{yx}{1+yx})
integral of 1/((x^2+36)^2)	\int\:\frac{1}{(x^{2}+36)^{2}}dx
laplacetransform 4t^3-24t+24sin(t)	laplacetransform\:4t^{3}-24t+24\sin(t)
limit as x approaches 1 of-f(x)	\lim\:_{x\to\:1}(-f(x))
integral of sec(x)tan(x)+4x	\int\:\sec(x)\tan(x)+4xdx
sum from n=0 to infinity of (1/4)^n	\sum\:_{n=0}^{\infty\:}(\frac{1}{4})^{n}
(\partial)/(\partial x)(e^{xyz^8})	\frac{\partial\:}{\partial\:x}(e^{xyz^{8}})
(\partial)/(\partial x)(6y^2)	\frac{\partial\:}{\partial\:x}(6y^{2})
derivative of f(x)=(3x^2-5x)e^x	derivative\:f(x)=(3x^{2}-5x)e^{x}
derivative of f(t)=(t^{62}+3t+3)(5t^2+4)	derivative\:f(t)=(t^{62}+3t+3)(5t^{2}+4)
derivative of sqrt(ln(7x))	\frac{d}{dx}(\sqrt{\ln(7x)})
(\partial)/(\partial x)((xy-1)^2)	\frac{\partial\:}{\partial\:x}((xy-1)^{2})
integral of (x^4+4)/(x^3)	\int\:\frac{x^{4}+4}{x^{3}}dx
y^{''}+3y^'+2y=e^{-2t}	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=e^{-2t}
integral of (x^2)/(sqrt((x^2+a^2)^3))	\int\:\frac{x^{2}}{\sqrt{(x^{2}+a^{2})^{3}}}dx
(sin(x)sin(2x)sin(3x))^'	(\sin(x)\sin(2x)\sin(3x))^{\prime\:}
derivative of y=e^xsin(2x)	derivative\:y=e^{x}\sin(2x)
limit as x approaches 0+of xln(sin(x))	\lim\:_{x\to\:0+}(x\ln(\sin(x)))
integral of 1/(sqrt(5x-2))	\int\:\frac{1}{\sqrt{5x-2}}dx
integral of 1/((1+u)^2)	\int\:\frac{1}{(1+u)^{2}}du
(dr)/(dθ)=8(cos(θ/3))^3	\frac{dr}{dθ}=8(\cos(\frac{θ}{3}))^{3}
limit as x approaches 0+of (e^x+x)^{2/x}	\lim\:_{x\to\:0+}((e^{x}+x)^{\frac{2}{x}})
y^{''}+10y^'+2500=500sin(100x)	y^{\prime\:\prime\:}+10y^{\prime\:}+2500=500\sin(100x)
derivative of ((x+1/(x-1))^{1/2})	\frac{d}{dx}((\frac{x+1}{x-1})^{\frac{1}{2}})
integral of 1/(sqrt(3x^2+4x+5))	\int\:\frac{1}{\sqrt{3x^{2}+4x+5}}dx
(\partial)/(\partial y)(3ye^{3x})	\frac{\partial\:}{\partial\:y}(3ye^{3x})
derivative of-ax	\frac{d}{dx}(-ax)
laplacetransform e^{7t}cos^2(t)	laplacetransform\:e^{7t}\cos^{2}(t)
(\partial)/(\partial x)(cos(8x)sin(3y))	\frac{\partial\:}{\partial\:x}(\cos(8x)\sin(3y))
limit as x approaches 0 of x/(sqrt(x))	\lim\:_{x\to\:0}(\frac{x}{\sqrt{x}})
integral of 4cos(2x)(sin(2x)+2)^3	\int\:4\cos(2x)(\sin(2x)+2)^{3}dx
derivative of x^2(e^x)	\frac{d}{dx}(x^{2}(e^{x}))
limit as h approaches 0 of ((sqrt(16+h))-4)/h	\lim\:_{h\to\:0}(\frac{(\sqrt{16+h})-4}{h})
integral of x(4+x^2)^{10}	\int\:x(4+x^{2})^{10}dx
limit as x approaches 1+of 5x+2p(x)	\lim\:_{x\to\:1+}(5x+2p(x))
(x+3)(dy)/(dx)+y=ln(x)	(x+3)\frac{dy}{dx}+y=\ln(x)
derivative of 3/(\sqrt[3]{x})	\frac{d}{dx}(\frac{3}{\sqrt[3]{x}})
limit as x approaches 0 of (sin(x^3))/x	\lim\:_{x\to\:0}(\frac{\sin(x^{3})}{x})
integral of cos^7(x)sin^6(x)	\int\:\cos^{7}(x)\sin^{6}(x)dx
derivative of sqrt(9+cot^2(x))	derivative\:\sqrt{9+\cot^{2}(x)}
derivative of x^2(1-2x)	derivative\:x^{2}(1-2x)
(1-x)(dy)/(dx)-xy=x+x^2	(1-x)\frac{dy}{dx}-xy=x+x^{2}
sum from n=0 to infinity of 1/(1.01^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{1.01^{n}}
integral from 1 to infinity of xe^{-8x}	\int\:_{1}^{\infty\:}xe^{-8x}dx
derivative of (4x-1^2)	\frac{d}{dx}((4x-1)^{2})
area y=x^2,y=2x^2-4x,y=0	area\:y=x^{2},y=2x^{2}-4x,y=0
integral of (x^2)/((x^2+8)^{3/2)}	\int\:\frac{x^{2}}{(x^{2}+8)^{\frac{3}{2}}}dx
(dr)/(dθ)=pi	\frac{dr}{dθ}=π
tangent of x^3-8x	tangent\:x^{3}-8x
integral of 18x^{1/2}	\int\:18x^{\frac{1}{2}}dx
(\partial)/(\partial x)(-1/((x-y)^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{(x-y)^{2}})
f(y)=cos(y)	f(y)=\cos(y)

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