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Popular Calculus Problems

derivative of sqrt(x^2-x+4)	\frac{d}{dx}(\sqrt{x^{2}-x+4})
integral of (e^x)/(e^x+5)	\int\:\frac{e^{x}}{e^{x}+5}dx
f(x)=arccot(sqrt(x))	f(x)=\arccot(\sqrt{x})
integral of x^{13}cos(x^7)	\int\:x^{13}\cos(x^{7})dx
derivative of (x^2-4x+3/(2x^2-3x+2))	\frac{d}{dx}(\frac{x^{2}-4x+3}{2x^{2}-3x+2})
(\partial)/(\partial y)(2x^2-x^4+y^2)	\frac{\partial\:}{\partial\:y}(2x^{2}-x^{4}+y^{2})
(\partial)/(\partial x)(2x^2+y^2+2xy+yx+7y)	\frac{\partial\:}{\partial\:x}(2x^{2}+y^{2}+2xy+yx+7y)
(\partial)/(\partial v)(ln(ucos(v)))	\frac{\partial\:}{\partial\:v}(\ln(u\cos(v)))
(\partial)/(\partial y)(ln(3xy)+x^2)	\frac{\partial\:}{\partial\:y}(\ln(3xy)+x^{2})
(\partial)/(\partial y)(y/((2x+3y)))	\frac{\partial\:}{\partial\:y}(\frac{y}{(2x+3y)})
limit as x approaches infinity of-1	\lim\:_{x\to\:\infty\:}(-1)
limit as x approaches 4 of 2x	\lim\:_{x\to\:4}(2x)
area 2x^2,x^4-2x^2	area\:2x^{2},x^{4}-2x^{2}
(\partial)/(\partial y)(1+3x+2y^2)	\frac{\partial\:}{\partial\:y}(1+3x+2y^{2})
derivative of (x+1/(x^2+1))	\frac{d}{dx}(\frac{x+1}{x^{2}+1})
derivative of y=-8	derivative\:y=-8
(\partial)/(\partial y)(m/y-625 y/x)	\frac{\partial\:}{\partial\:y}(\frac{m}{y}-625\frac{y}{x})
derivative of f(x)=x^3(x^2+4)^{-2}	derivative\:f(x)=x^{3}(x^{2}+4)^{-2}
derivative of 4*e^{2x}	derivative\:4\cdot\:e^{2x}
derivative of 1-3/y+x	\frac{d}{dx}(1-\frac{3}{y}+x)
integral from 0 to 1 of 2sqrt(x)-2x	\int\:_{0}^{1}2\sqrt{x}-2xdx
integral of (x^3-1)/(x^4-4x+1)	\int\:\frac{x^{3}-1}{x^{4}-4x+1}dx
(dy)/(dx)+(3/x)y=-2x-7	\frac{dy}{dx}+(\frac{3}{x})y=-2x-7
area 3sin(x),4cos(x),[0,0.8pi]	area\:3\sin(x),4\cos(x),[0,0.8π]
derivative of-4sec^2(x+6sec^4(x))	\frac{d}{dx}(-4\sec^{2}(x)+6\sec^{4}(x))
limit as x approaches 3 of-3x-7	\lim\:_{x\to\:3}(-3x-7)
derivative of e^u	derivative\:e^{u}
integral of cos^{10}(x)	\int\:\cos^{10}(x)dx
integral of (4x-1)/(x^2+2x+5)	\int\:\frac{4x-1}{x^{2}+2x+5}dx
(\partial)/(\partial y)(-6x)	\frac{\partial\:}{\partial\:y}(-6x)
integral of 5/(x^4)	\int\:\frac{5}{x^{4}}dx
derivative of 5/(\sqrt[3]{x}-6/(2^x))	\frac{d}{dx}(\frac{5}{\sqrt[3]{x}}-\frac{6}{2^{x}})
y^'-3/2 y=3t+2e^t	y^{\prime\:}-\frac{3}{2}y=3t+2e^{t}
derivative of-14e^{-x^2}x	derivative\:-14e^{-x^{2}}x
3(y^4+1)dx+(4xy^3)dy=0	3(y^{4}+1)dx+(4xy^{3})dy=0
limit as x approaches-2 of x^2+2x-1	\lim\:_{x\to\:-2}(x^{2}+2x-1)
integral of 1/((y-1))	\int\:\frac{1}{(y-1)}dy
integral of x^3(x^4-9)^4	\int\:x^{3}(x^{4}-9)^{4}dx
limit as x approaches 4 of sqrt(20-x^2)	\lim\:_{x\to\:4}(\sqrt{20-x^{2}})
(\partial)/(\partial y)(x^2+y^2+z^2-1)	\frac{\partial\:}{\partial\:y}(x^{2}+y^{2}+z^{2}-1)
derivative of 6sin(x)-8e^x	derivative\:6\sin(x)-8e^{x}
(dy)/(dx)=cos(x)(1+3y)	\frac{dy}{dx}=\cos(x)(1+3y)
(\partial)/(\partial x)(x^6y^6+4x^6y)	\frac{\partial\:}{\partial\:x}(x^{6}y^{6}+4x^{6}y)
(\partial)/(\partial x)(x*e^{-x^2-y^2})	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{-x^{2}-y^{2}})
integral of xsqrt(2-x^2)	\int\:x\sqrt{2-x^{2}}dx
(x^2dy)/(dx)=y-xy,y[-1]=-4	\frac{x^{2}dy}{dx}=y-xy,y[-1]=-4
(\partial)/(\partial x)((sin(x))/(y^2))	\frac{\partial\:}{\partial\:x}(\frac{\sin(x)}{y^{2}})
(\partial)/(\partial u(v))((e^v)/(u(v)+v^7))	\frac{\partial\:}{\partial\:u(v)}(\frac{e^{v}}{u(v)+v^{7}})
integral of 1/(sqrt(x^2-169))	\int\:\frac{1}{\sqrt{x^{2}-169}}dx
integral from 2 to 4 of x/6 (2x-3)	\int\:_{2}^{4}\frac{x}{6}(2x-3)dx
integral from-2 to 2 of (12)/(x^2-4x-32)	\int\:_{-2}^{2}\frac{12}{x^{2}-4x-32}dx
derivative of sin^2(x^3)	\frac{d}{dx}(\sin^{2}(x^{3}))
derivative of 4xlog_{10}(x^9)	derivative\:4x\log_{10}(x^{9})
integral of (5x^7-9x^5)/(x^3)	\int\:\frac{5x^{7}-9x^{5}}{x^{3}}dx
derivative of f(x)=(2x)/(2+sqrt(x))	derivative\:f(x)=\frac{2x}{2+\sqrt{x}}
(\partial)/(\partial x)(4xcos(y))	\frac{\partial\:}{\partial\:x}(4x\cos(y))
laplacetransform 5sin(4t)	laplacetransform\:5\sin(4t)
(\partial)/(\partial z)(x^y)	\frac{\partial\:}{\partial\:z}(x^{y})
(x^2+1)(dy)/(dx)+3x(y-1)=0	(x^{2}+1)\frac{dy}{dx}+3x(y-1)=0
integral from 1 to 10 of 1/(4x^3)	\int\:_{1}^{10}\frac{1}{4x^{3}}dx
derivative of 10x+1	\frac{d}{dx}(10x+1)
derivative of 7x^2e^{-x}	\frac{d}{dx}(7x^{2}e^{-x})
limit as x approaches-0 of e^{-1/x}	\lim\:_{x\to\:-0}(e^{-\frac{1}{x}})
integral from 2 to-1 of 3x(x-4)	\int\:_{2}^{-1}3x(x-4)dx
integral from 0 to 1 of 1/(x+1)	\int\:_{0}^{1}\frac{1}{x+1}dx
integral of xsqrt(x-1)	\int\:x\sqrt{x-1}dx
tangent of x^2-5	tangent\:x^{2}-5
limit as x approaches 5 of 500	\lim\:_{x\to\:5}(500)
limit as x approaches 3+of ln(x)	\lim\:_{x\to\:3+}(\ln(x))
(dy)/(dx)=3x-2y+3	\frac{dy}{dx}=3x-2y+3
derivative of 10^6x^2e^{-x}	\frac{d}{dx}(10^{6}x^{2}e^{-x})
derivative of (4x+9/x ^2)	\frac{d}{dx}((4x+\frac{9}{x})^{2})
derivative of e^x+e^y	\frac{d}{dx}(e^{x}+e^{y})
derivative of log_{10}(x^2+x+1)	\frac{d}{dx}(\log_{10}(x^{2}+x+1))
tangent of f(x)=(2x+3)/(3x-2)	tangent\:f(x)=\frac{2x+3}{3x-2}
integral from 0 to 2 of 1/(8+2x^2)	\int\:_{0}^{2}\frac{1}{8+2x^{2}}dx
area 3ln(x),xln(x),1,2	area\:3\ln(x),x\ln(x),1,2
(dy}{dx}=-\frac{e^x)/8	\frac{dy}{dx}=-\frac{e^{x}}{8}
integral of sec^2(3x)tan^3(3x)	\int\:\sec^{2}(3x)\tan^{3}(3x)dx
derivative of x*6^x	derivative\:x\cdot\:6^{x}
(\partial)/(\partial y)(x/(7+y))	\frac{\partial\:}{\partial\:y}(\frac{x}{7+y})
integral of sin^3(x)*cos^4(x)	\int\:\sin^{3}(x)\cdot\:\cos^{4}(x)dx
derivative of arctan(xdx)	\frac{d}{dx}(\arctan(x)dx)
integral of 3sin^2(xco)s^2x	\int\:3\sin^{2}(xco)s^{2}xdx
(\partial)/(\partial y)(-cos(y))	\frac{\partial\:}{\partial\:y}(-\cos(y))
derivative of 0.1*x^4	\frac{d}{dx}(0.1\cdot\:x^{4})
derivative of cos(x)+sin(x)+1/2 x^2+1/x	derivative\:\cos(x)+\sin(x)+\frac{1}{2}x^{2}+\frac{1}{x}
laplacetransform x*e^x	laplacetransform\:x\cdot\:e^{x}
d/(dt)(cos(120pi)t)	\frac{d}{dt}(\cos(120π)t)
integral from 0 to l of sin^2((npix)/l)	\int\:_{0}^{l}\sin^{2}(\frac{nπx}{l})dx
integral of cos(sqrt(1-x))	\int\:\cos(\sqrt{1-x})dx
derivative of 2/((1-x^2))	\frac{d}{dx}(\frac{2}{(1-x)^{2}})
integral of (x^3-2)/(x^2+3x+2)	\int\:\frac{x^{3}-2}{x^{2}+3x+2}dx
derivative of 1/(x^3-2x)	\frac{d}{dx}(\frac{1}{x^{3}-2x})
limit as n approaches infinity of-1^n	\lim\:_{n\to\:\infty\:}(-1^{n})
integral from 0 to pi of 4sin(x)+sin(4x)	\int\:_{0}^{π}4\sin(x)+\sin(4x)dx
(\partial)/(\partial y)(1-3/x+y)	\frac{\partial\:}{\partial\:y}(1-\frac{3}{x}+y)
limit as x approaches 0 of (x^3-8)/(x-2)	\lim\:_{x\to\:0}(\frac{x^{3}-8}{x-2})
integral of e^x+20(1+x^2)^{-1}	\int\:e^{x}+20(1+x^{2})^{-1}dx
derivative of sin(x/4)	\frac{d}{dx}(\sin(\frac{x}{4}))

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