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Popular Calculus Problems

(\partial)/(\partial x)(cos(x-y^2))	\frac{\partial\:}{\partial\:x}(\cos(x-y^{2}))
sum from n=3 to infinity of 1/(esqrt(n))	\sum\:_{n=3}^{\infty\:}\frac{1}{e\sqrt{n}}
(dy)/(dx)=0.0013y(2500-y)	\frac{dy}{dx}=0.0013y(2500-y)
(dy)/(dt)=100-y	\frac{dy}{dt}=100-y
integral from 0 to 3 of 9	\int\:_{0}^{3}9
integral of x(15x+8)	\int\:x(15x+8)dx
(\partial)/(\partial x)(3/(xy^2))	\frac{\partial\:}{\partial\:x}(\frac{3}{xy^{2}})
inverse oflaplace arctan(s)+1	inverselaplace\:\arctan(s)+1
limit as x approaches 0 of x-sin(x)	\lim\:_{x\to\:0}(x-\sin(x))
(6xy^2-3)dx+(6x^2y+4)dy=0	(6xy^{2}-3)dx+(6x^{2}y+4)dy=0
integral of (cos(x)-(sin(x))/x)/(x)	\int\:\frac{\cos(x)-\frac{\sin(x)}{x}}{x}dx
derivative of (6x^3/(3x^2-3))	\frac{d}{dx}(\frac{6x^{3}}{3x^{2}-3})
(\partial)/(\partial x)(-2xy(6-x-y))	\frac{\partial\:}{\partial\:x}(-2xy(6-x-y))
limit as x approaches 2 of (-4)/(2-x)	\lim\:_{x\to\:2}(\frac{-4}{2-x})
limit as x approaches 0 of log_{3}(x)	\lim\:_{x\to\:0}(\log_{3}(x))
derivative of sqrt(4x+1)	derivative\:\sqrt{4x+1}
d/(dm)(16m^2+40m+25)	\frac{d}{dm}(16m^{2}+40m+25)
derivative of sqrt(3x^2)sin(5x)	\frac{d}{dx}(\sqrt{3x^{2}}\sin(5x))
integral of (2x-3)/((x^2-3x+6)^2)	\int\:\frac{2x-3}{(x^{2}-3x+6)^{2}}dx
integral of tan(x)-x	\int\:\tan(x)-xdx
limit as x approaches 4 of x/(x^2+4)	\lim\:_{x\to\:4}(\frac{x}{x^{2}+4})
derivative of arctan(sqrt(3x))	derivative\:\arctan(\sqrt{3x})
integral of ((36-25x^2)^{3/2})/(x^6)	\int\:\frac{(36-25x^{2})^{\frac{3}{2}}}{x^{6}}dx
derivative of (4(-x^2+4)/((x^2+4)^2))	\frac{d}{dx}(\frac{4(-x^{2}+4)}{(x^{2}+4)^{2}})
derivative of sin(5x)+sin(2)(5x)	derivative\:\sin(5x)+\sin(2)(5x)
derivative of 2xcos(x)-x^2sin(x)	derivative\:2x\cos(x)-x^{2}\sin(x)
limit as x approaches 3 of (8)+6(-7)	\lim\:_{x\to\:3}((8)+6(-7))
integral of 5x^3cos(x^2)	\int\:5x^{3}\cos(x^{2})dx
limit as x approaches 2 of (2-x)^{x-2}	\lim\:_{x\to\:2}((2-x)^{x-2})
(arctan(9x))^2	(\arctan(9x))^{2}
laplacetransform (t-8)^3	laplacetransform\:(t-8)^{3}
(dy)/(dx)=(3x^2+4x-4)/(2y-4),y(1)=3	\frac{dy}{dx}=\frac{3x^{2}+4x-4}{2y-4},y(1)=3
sum from n=3 to infinity of 1/2*(5/7)^n	\sum\:_{n=3}^{\infty\:}\frac{1}{2}\cdot\:(\frac{5}{7})^{n}
integral of sec^2(x)sin(x)	\int\:\sec^{2}(x)\sin(x)dx
integral of x^{0.5}	\int\:x^{0.5}dx
integral of 1/(x^3+4x)	\int\:\frac{1}{x^{3}+4x}dx
derivative of f(x)=4x^{5/4}+8x^{3/2}+2x	derivative\:f(x)=4x^{\frac{5}{4}}+8x^{\frac{3}{2}}+2x
tangent of f(x)= 2/(sqrt(x)),\at 1/16	tangent\:f(x)=\frac{2}{\sqrt{x}},\at\:\frac{1}{16}
derivative of ((x^2+x)/(x^2))	\frac{d}{dx}(\frac{(x^{2}+x)}{x^{2}})
integral of (x^5-10x^4+x^3-15x^2)	\int\:(x^{5}-10x^{4}+x^{3}-15x^{2})dx
sum from n=1 to infinity of (z^n)/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{z^{n}}{n^{2}}
integral of e^{x^4}x^3	\int\:e^{x^{4}}x^{3}dx
(dy)/(dx)=x+3	\frac{dy}{dx}=x+3
limit as x approaches 2 of 4x	\lim\:_{x\to\:2}(4x)
integral from 1 to 4 of (1/x)^2	\int\:_{1}^{4}(\frac{1}{x})^{2}dx
tangent of ysqrt(x)+y^2=2x,(4,2)	tangent\:y\sqrt{x}+y^{2}=2x,(4,2)
derivative of (2x^2-x-1sqrt(x))	\frac{d}{dx}((2x^{2}-x-1)\sqrt{x})
derivative of x(4x+3)^{1/3}	derivative\:x(4x+3)^{\frac{1}{3}}
derivative of e^x-7x^6	derivative\:e^{x}-7x^{6}
derivative of cot(6sqrt(-u))	derivative\:\cot(6\sqrt{-u})
limit as x approaches 0 of x^2+x	\lim\:_{x\to\:0}(x^{2}+x)
integral of (6/5)^x	\int\:(\frac{6}{5})^{x}dx
derivative of 2θ	derivative\:2θ
derivative of 2x^2sin(x+2xcos(x))	\frac{d}{dx}(2x^{2}\sin(x)+2x\cos(x))
integral of sqrt(x+1)	\int\:\sqrt{x+1}dx
integral of sec^2(x)+sec(x)tan(x)	\int\:\sec^{2}(x)+\sec(x)\tan(x)dx
integral of pi/2 (x+cos(x))	\int\:\frac{π}{2}(x+\cos(x))dx
derivative of x^2-4x+1	\frac{d}{dx}(x^{2}-4x+1)
integral of tan(2)(x)	\int\:\tan(2)(x)dx
integral of xsqrt(2x^2+7)	\int\:x\sqrt{2x^{2}+7}dx
(\partial)/(\partial t)(2st)	\frac{\partial\:}{\partial\:t}(2st)
f(t)=5t^2+31t+100	f(t)=5t^{2}+31t+100
derivative of-(3x)/y	derivative\:-\frac{3x}{y}
derivative of f(x)=x^2+x-1	derivative\:f(x)=x^{2}+x-1
(dy)/(dx)=e^{6y+6x}	\frac{dy}{dx}=e^{6y+6x}
inverse oflaplace (s+5)/(s(s^2+8s+25))	inverselaplace\:\frac{s+5}{s(s^{2}+8s+25)}
simplify 1/(3x^{2/3)}+2	simplify\:\frac{1}{3x^{\frac{2}{3}}}+2
integral of 3x(x^2+6)^2	\int\:3x(x^{2}+6)^{2}dx
(\partial)/(\partial y)(5cos(xy^2))	\frac{\partial\:}{\partial\:y}(5\cos(xy^{2}))
derivative of 2/3	derivative\:\frac{2}{3}
limit as x approaches 1/2 of 2x+1	\lim\:_{x\to\:\frac{1}{2}}(2x+1)
(\partial)/(\partial x)(4xy^3)	\frac{\partial\:}{\partial\:x}(4xy^{3})
tangent of y= 1/(x-6),(-2,-1/8)	tangent\:y=\frac{1}{x-6},(-2,-\frac{1}{8})
integral of (2x-1)^3	\int\:(2x-1)^{3}dx
(dy)/(dt)=t^2y^3	\frac{dy}{dt}=t^{2}y^{3}
derivative of x^3(3x-8)	\frac{d}{dx}(x^{3}(3x-8))
integral from 6 to 11 of 10arccot(x)	\int\:_{6}^{11}10\arccot(x)dx
derivative of f(x)=sin(sin(8e^x))	derivative\:f(x)=\sin(\sin(8e^{x}))
integral of 1/(sqrt(u^2-a^2))	\int\:\frac{1}{\sqrt{u^{2}-a^{2}}}du
derivative of x^8(x-4)^7	derivative\:x^{8}(x-4)^{7}
derivative of cos(2^{3x^2+5x-6})	\frac{d}{dx}(\cos(2^{3x^{2}+5x-6}))
(18+x^2)y^'-2xy=0	(18+x^{2})y^{\prime\:}-2xy=0
y^'=y(xy^6+2)	y^{\prime\:}=y(xy^{6}+2)
y^'=(4t^3+1)/(2y-6)	y^{\prime\:}=\frac{4t^{3}+1}{2y-6}
(\partial)/(\partial y)(x^2y^3-1/(1+9x^2))	\frac{\partial\:}{\partial\:y}(x^{2}y^{3}-\frac{1}{1+9x^{2}})
tangent of f(x)= 6/(x-1),\at x=3	tangent\:f(x)=\frac{6}{x-1},\at\:x=3
derivative of f(x)=(16x)^3	derivative\:f(x)=(16x)^{3}
f^'(x)=5x^4	f^{\prime\:}(x)=5x^{4}
derivative of (2log_{2}(x))/(ln(2)x)	derivative\:\frac{2\log_{2}(x)}{\ln(2)x}
derivative of (6x^2+8x+6)/(sqrt(x))	derivative\:\frac{6x^{2}+8x+6}{\sqrt{x}}
(d^2)/(dx^2)(15e^{1/x})	\frac{d^{2}}{dx^{2}}(15e^{\frac{1}{x}})
integral of cos^3(θ)sin(θ)	\int\:\cos^{3}(θ)\sin(θ)dθ
xy^{''}+2y^'=0	xy^{\prime\:\prime\:}+2y^{\prime\:}=0
derivative of 1/3 (x^2+2^{2/3})	\frac{d}{dx}(\frac{1}{3}(x^{2}+2)^{\frac{2}{3}})
sum from n=1 to infinity of (n^3)/(2^n)	\sum\:_{n=1}^{\infty\:}\frac{n^{3}}{2^{n}}
derivative of ln(x^2)	\frac{d}{dx}(\ln(x^{2}))
(\partial)/(\partial y)(x^4y+xz-yz^2-7)	\frac{\partial\:}{\partial\:y}(x^{4}y+xz-yz^{2}-7)
(dy)/(dx)=e^{6y}e^{6x}	\frac{dy}{dx}=e^{6y}e^{6x}
(dy)/(dx)=y(y^5x+2)	\frac{dy}{dx}=y(y^{5}x+2)
sqrt(1-4x^2)y^'=x	\sqrt{1-4x^{2}}y^{\prime\:}=x

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