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Popular Calculus Problems

(dy)/(dx)=((e^{x-y}))/(1+e^x)	\frac{dy}{dx}=\frac{(e^{x-y})}{1+e^{x}}
integral from 0 to 2 of 30000e^{0.03x}	\int\:_{0}^{2}30000e^{0.03x}dx
integral of 36t^8e^{-t^9}	\int\:36t^{8}e^{-t^{9}}dt
limit as x approaches-1 of sqrt(5-11x)	\lim\:_{x\to\:-1}(\sqrt{5-11x})
tangent of x^2+5	tangent\:x^{2}+5
derivative of (x^3/3+7x^2+50x)	\frac{d}{dx}(\frac{x^{3}}{3}+7x^{2}+50x)
(\partial)/(\partial x)(5arccot(x))	\frac{\partial\:}{\partial\:x}(5\arccot(x))
derivative of (2x-8^4(x^2+x+1)^5)	\frac{d}{dx}((2x-8)^{4}(x^{2}+x+1)^{5})
integral of (e^{x-y})/(1+e^x)	\int\:\frac{e^{x-y}}{1+e^{x}}
derivative of log_{3}(3x-7)	\frac{d}{dx}(\log_{3}(3x-7))
(dy)/(dt)=-y/t+2	\frac{dy}{dt}=-\frac{y}{t}+2
implicit (dy)/(dx),xy+x=2	implicit\:\frac{dy}{dx},xy+x=2
integral from 5 to 8 of 5/(sqrt(x-5))	\int\:_{5}^{8}\frac{5}{\sqrt{x-5}}dx
(\partial)/(\partial x)(u/(1+2.4(x/y)))	\frac{\partial\:}{\partial\:x}(\frac{u}{1+2.4(\frac{x}{y})})
(\partial)/(\partial x)(6x^5y^6+5x^4y^7)	\frac{\partial\:}{\partial\:x}(6x^{5}y^{6}+5x^{4}y^{7})
integral from 0 to 3 of 15x	\int\:_{0}^{3}15xdx
limit as x approaches-2 of (x^2-6)/(2-x)	\lim\:_{x\to\:-2}(\frac{x^{2}-6}{2-x})
inverse oflaplace 1/(s^3+s^2)	inverselaplace\:\frac{1}{s^{3}+s^{2}}
derivative of 3^{1-2n}	derivative\:3^{1-2n}
(\partial)/(\partial x)(3xy-x^2y^2+23)	\frac{\partial\:}{\partial\:x}(3xy-x^{2}y^{2}+23)
(dy)/(dx)=(sqrt(x))/(e^y)	\frac{dy}{dx}=\frac{\sqrt{x}}{e^{y}}
derivative of sqrt(3x^2-2)	derivative\:\sqrt{3x^{2}-2}
derivative of f(x)=-9.8x^2+2x+1	derivative\:f(x)=-9.8x^{2}+2x+1
integral of 1/(arcsin(x)sqrt(1-x^2))	\int\:\frac{1}{\arcsin(x)\sqrt{1-x^{2}}}dx
(\partial)/(\partial x)(x^2+xy+y^2+2x-y)	\frac{\partial\:}{\partial\:x}(x^{2}+xy+y^{2}+2x-y)
d/(dt)(-cos(2t))	\frac{d}{dt}(-\cos(2t))
integral of (2x^4-8x^3)*e^{-3x}	\int\:(2x^{4}-8x^{3})\cdot\:e^{-3x}dx
(2xy)dy+(x^2+y^2)dx=0	(2xy)dy+(x^{2}+y^{2})dx=0
derivative of y=(tan(x))^{9/x}	derivative\:y=(\tan(x))^{\frac{9}{x}}
integral of (x^2sqrt(x))	\int\:(x^{2}\sqrt{x})dx
derivative of 6x^{1/4}	derivative\:6x^{\frac{1}{4}}
integral of (3x)/((1-x^2)^3)	\int\:\frac{3x}{(1-x^{2})^{3}}dx
(\partial)/(\partial x)(cos^2(x))	\frac{\partial\:}{\partial\:x}(\cos^{2}(x))
derivative of (x^2(x^2+9x))^6	derivative\:(x^{2}(x^{2}+9x))^{6}
(\partial)/(\partial x)(ln(x+y^2))	\frac{\partial\:}{\partial\:x}(\ln(x+y^{2}))
(\partial)/(\partial x)((2xy)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{2xy}{x+y})
integral of wsqrt(w^2-ln(3))	\int\:w\sqrt{w^{2}-\ln(3)}dw
limit as x approaches 0 of (3x)/(xe^x)	\lim\:_{x\to\:0}(\frac{3x}{xe^{x}})
integral of (3x^2-2x+5)/(x^2)	\int\:\frac{3x^{2}-2x+5}{x^{2}}dx
derivative of f(x)=x^3sqrt(x)	derivative\:f(x)=x^{3}\sqrt{x}
limit as x approaches-3+of sqrt(x^3+27)	\lim\:_{x\to\:-3+}(\sqrt{x^{3}+27})
integral from 0 to 8 of e^xsin(x)	\int\:_{0}^{8}e^{x}\sin(x)dx
limit as x approaches 0+of x^{x^5}	\lim\:_{x\to\:0+}(x^{x^{5}})
derivative of 2cos(x+sin(2x))	\frac{d}{dx}(2\cos(x)+\sin(2x))
derivative of ax+b/x	\frac{d}{dx}(ax+\frac{b}{x})
derivative of (e^x/(x^2-1))	\frac{d}{dx}(\frac{e^{x}}{x^{2}-1})
integral of x*sin(x)cos(x)	\int\:x\cdot\:\sin(x)\cos(x)dx
sum from n=7 to infinity of 1/(nln(n))	\sum\:_{n=7}^{\infty\:}\frac{1}{n\ln(n)}
integral from 0 to 3 of \|x^2-9\|	\int\:_{0}^{3}\left\|x^{2}-9\right\|dx
integral of-e^{-2x}	\int\:-e^{-2x}dx
derivative of (64)/(x^2+16)	derivative\:\frac{64}{x^{2}+16}
tangent of f(x)=x^2-4x,\at x=1	tangent\:f(x)=x^{2}-4x,\at\:x=1
derivative of-5sin(x)	\frac{d}{dx}(-5\sin(x))
(\partial)/(\partial x)(sqrt(2-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{2-x^{2}-y^{2}})
derivative of-e^{-4x}	\frac{d}{dx}(-e^{-4x})
integral from 3 to infinity of (e^{-1/x})/(x^2)	\int\:_{3}^{\infty\:}\frac{e^{-\frac{1}{x}}}{x^{2}}dx
(cos(x))^'	(\cos(x))^{\prime\:}
integral of (sqrt(x)+1)	\int\:(\sqrt{x}+1)dx
integral of (2^x+4e^x+x^3+5)	\int\:(2^{x}+4e^{x}+x^{3}+5)dx
integral from 6 to 8 of (10)/((x-6)^3)	\int\:_{6}^{8}\frac{10}{(x-6)^{3}}dx
derivative of f(x)=x^2e^{-7x}	derivative\:f(x)=x^{2}e^{-7x}
integral of x^2*2x	\int\:x^{2}\cdot\:2xdx
integral from 0 to 7 of (7t)/((t-8)^2)	\int\:_{0}^{7}\frac{7t}{(t-8)^{2}}dt
simplify-3	simplify\:-3
f(x)=arccos(e^x)	f(x)=\arccos(e^{x})
integral of 2e^x-6x	\int\:2e^{x}-6xdx
6t(dy)/(dt)+y=0	6t\frac{dy}{dt}+y=0
derivative of 1/3 sin^3(x)	\frac{d}{dx}(\frac{1}{3}\sin^{3}(x))
integral of ycos(xy)	\int\:y\cos(xy)dx
derivative of 3sec^2(x)	\frac{d}{dx}(3\sec^{2}(x))
(dy)/(dx)=cos(5x)	\frac{dy}{dx}=\cos(5x)
derivative of tan(u)	derivative\:\tan(u)
derivative of 100(1+Ae^{-t})^{-1}	derivative\:100(1+Ae^{-t})^{-1}
integral of t^2cos(2t)	\int\:t^{2}\cos(2t)dt
derivative of (-x^3-x^2+xcos(x))	\frac{d}{dx}((-x^{3}-x^{2}+x)\cos(x))
inverse oflaplace 1/(p(p+1))	inverselaplace\:\frac{1}{p(p+1)}
tangent of y=tan(18x^2),\at x=sqrt(pi)	tangent\:y=\tan(18x^{2}),\at\:x=\sqrt{π}
y^{''}+9y=csc^2(3t)	y^{\prime\:\prime\:}+9y=\csc^{2}(3t)
inverse oflaplace 5/(s^2+4)	inverselaplace\:\frac{5}{s^{2}+4}
derivative of ln(x^{11})	\frac{d}{dx}(\ln(x^{11}))
(\partial)/(\partial x)(x^2y^3(6-x-y))	\frac{\partial\:}{\partial\:x}(x^{2}y^{3}(6-x-y))
derivative of x^{15}	\frac{d}{dx}(x^{15})
integral of 4e^6	\int\:4e^{6}dx
integral of (7cos(x)+2sin(x))	\int\:(7\cos(x)+2\sin(x))dx
y^{''}+4y=sin(2t)cos(2t)	y^{\prime\:\prime\:}+4y=\sin(2t)\cos(2t)
integral of z/(z^4+4)	\int\:\frac{z}{z^{4}+4}dz
(dy)/(dx)=(x+y-3)^2	\frac{dy}{dx}=(x+y-3)^{2}
taylor cos(x),0	taylor\:\cos(x),0
derivative of x^3+(4x^2/3-2x+5)	\frac{d}{dx}(x^{3}+\frac{4x^{2}}{3}-2x+5)
integral of e^{2x}*2	\int\:e^{2x}\cdot\:2dx
integral of 6/(x(x-6)^2)	\int\:\frac{6}{x(x-6)^{2}}dx
y^{''}+4y^'+5y=15x+3e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=15x+3e^{-x}
y^{''}+8y^'+7y=-8-x+24x^2+7x^3	y^{\prime\:\prime\:}+8y^{\prime\:}+7y=-8-x+24x^{2}+7x^{3}
integral of x^2*sqrt(1-x^2)	\int\:x^{2}\cdot\:\sqrt{1-x^{2}}dx
integral of (1+cos^2(x))	\int\:(1+\cos^{2}(x))dx
limit as x approaches infinity of 5e^{-t}i-(5t)/(t+7)j+5arctan(tk)	\lim\:_{x\to\:\infty\:}(5e^{-t}i-\frac{5t}{t+7}j+5\arctan(tk))
(\partial)/(\partial x)(x^2+y^2+3xy+5x)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+3xy+5x)
x^2y^'+(2-y)=0	x^{2}y^{\prime\:}+(2-y)=0
(\partial)/(\partial y)(2xe^{-y})	\frac{\partial\:}{\partial\:y}(2xe^{-y})
(\partial)/(\partial x)(7xy^3+5)	\frac{\partial\:}{\partial\:x}(7xy^{3}+5)

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