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Popular Calculus Problems

limit as x approaches 2 of sqrt(2x-4)+8	\lim\:_{x\to\:2}(\sqrt{2x-4}+8)
integral of (cot(x))	\int\:(\cot(x))dx
derivative of 8/(3x^2+3/(2x)+2)	\frac{d}{dx}(\frac{8}{3x^{2}}+\frac{3}{2x}+2)
derivative of 3x+7	derivative\:3x+7
f^'(x)=x^4(x-2)(x+3)	f^{\prime\:}(x)=x^{4}(x-2)(x+3)
integral of 10sqrt(x)+sqrt(11)	\int\:10\sqrt{x}+\sqrt{11}dx
integral of x^2\|8x^3+1\|	\int\:x^{2}\left\|8x^{3}+1\right\|dx
derivative of 2sec(x-7x)	\frac{d}{dx}(2\sec(x)-7x)
slope of (-2,-3),(4,6)	slope\:(-2,-3),(4,6)
integral of 1/(a^2+x^2)	\int\:\frac{1}{a^{2}+x^{2}}dx
derivative of (5t^2)/2+t+6	derivative\:\frac{5t^{2}}{2}+t+6
d/(dt)(4te^{3t})	\frac{d}{dt}(4te^{3t})
slope of y=x^2-3x-5	slope\:y=x^{2}-3x-5
integral of cos(pi/3 x)	\int\:\cos(\frac{π}{3}x)dx
integral of x/(sqrt(-7-8x-x^2))	\int\:\frac{x}{\sqrt{-7-8x-x^{2}}}dx
integral from 0 to 5 of 5x	\int\:_{0}^{5}5xdx
derivative of x*sin(3x)	\frac{d}{dx}(x\cdot\:\sin(3x))
derivative of x^4+4	\frac{d}{dx}(x^{4}+4)
derivative of x-y+1	\frac{d}{dx}(x-y+1)
(\partial)/(\partial y)(4y^2)	\frac{\partial\:}{\partial\:y}(4y^{2})
derivative of ln(5x^2)	\frac{d}{dx}(\ln(5x^{2}))
slope of (x^2+y^2)^2=4x^2y	slope\:(x^{2}+y^{2})^{2}=4x^{2}y
derivative of \sqrt[3]{x^2}sin(5x)	\frac{d}{dx}(\sqrt[3]{x^{2}}\sin(5x))
derivative of arctanh(x)	\frac{d}{dx}(\arctanh(x))
integral of 5xln(5x)	\int\:5x\ln(5x)dx
integral of 1/(2x^2)	\int\:\frac{1}{2x^{2}}dx
area y=(7t-4),(0,0.5)	area\:y=(7t-4),(0,0.5)
derivative of x^{tan(x})	\frac{d}{dx}(x^{\tan(x)})
integral from 1 to 9 of 2/(sqrt(x))	\int\:_{1}^{9}\frac{2}{\sqrt{x}}dx
derivative of 2/3 x^2(x^3-1)	\frac{d}{dx}(\frac{2}{3}x^{2}(x^{3}-1))
integral of (x^3+x^2-x)	\int\:(x^{3}+x^{2}-x)dx
integral of (cos(x))/(9-sin(x))	\int\:\frac{\cos(x)}{9-\sin(x)}dx
derivative of 3x(10x^3-6/(x+10))	\frac{d}{dx}(3x(10x^{3}-\frac{6}{x+10}))
derivative of-5cos(5x)	\frac{d}{dx}(-5\cos(5x))
limit as x approaches-infinity of 5^x+2	\lim\:_{x\to\:-\infty\:}(5^{x}+2)
integral from 0 to 1/2 of 3arccos(x)	\int\:_{0}^{\frac{1}{2}}3\arccos(x)dx
(\partial)/(\partial y)(x*ln(y-z))	\frac{\partial\:}{\partial\:y}(x\cdot\:\ln(y-z))
integral of (x^3)/(x^4+3x^2+2)	\int\:\frac{x^{3}}{x^{4}+3x^{2}+2}dx
integral from 1 to 7 of 1/(36+(x+5)^2)	\int\:_{1}^{7}\frac{1}{36+(x+5)^{2}}dx
derivative of (x^2-4/(x^2+4))	\frac{d}{dx}(\frac{x^{2}-4}{x^{2}+4})
integral of (-2x^4-4x^2-5)	\int\:(-2x^{4}-4x^{2}-5)dx
integral of 2cos(x/2)	\int\:2\cos(\frac{x}{2})dx
(\partial)/(\partial y)(2ln(x)+ln(y))	\frac{\partial\:}{\partial\:y}(2\ln(x)+\ln(y))
(\partial)/(\partial x)(sqrt(x/y))	\frac{\partial\:}{\partial\:x}(\sqrt{\frac{x}{y}})
integral from-1 to 1 of e^{x^2}	\int\:_{-1}^{1}e^{x^{2}}dx
integral of x^4-2x^2-4x	\int\:x^{4}-2x^{2}-4xdx
expand (e^x-2)/((1-e^{-x))^2}	expand\:\frac{e^{x}-2}{(1-e^{-x})^{2}}
derivative of (x^2-2^{-3})	\frac{d}{dx}((x^{2}-2)^{-3})
(\partial)/(\partial x)(1/(2y))	\frac{\partial\:}{\partial\:x}(\frac{1}{2y})
integral of-xe^{-x^2}	\int\:-xe^{-x^{2}}dx
tangent of f(x)=x^2+x,\at x=-2	tangent\:f(x)=x^{2}+x,\at\:x=-2
2x(dy)/(dx)=y	2x\frac{dy}{dx}=y
limit as x approaches 1/3 of \|3x-1\|-5	\lim\:_{x\to\:\frac{1}{3}}(\left\|3x-1\right\|-5)
3x^2y^2dx+(2y^3x+4y^3)dy=0	3x^{2}y^{2}dx+(2y^{3}x+4y^{3})dy=0
5x^{''}+25x^'+1700x=0	5x^{\prime\:\prime\:}+25x^{\prime\:}+1700x=0
1/(y^{1/3)}dy=1dx	\frac{1}{y^{\frac{1}{3}}}dy=1dx
integral of-4sin(2x)+3cos(3x)	\int\:-4\sin(2x)+3\cos(3x)dx
limit as x approaches 0+of xsin(1/x)	\lim\:_{x\to\:0+}(x\sin(\frac{1}{x}))
derivative of P(t)=0.45t^2-12t+105	derivative\:P(t)=0.45t^{2}-12t+105
derivative of (cos(x)sin(x))	\frac{d}{dx}((\cos(x))\sin(x))
integral of (1/x-5x)	\int\:(\frac{1}{x}-5x)dx
t(dy)/(dt)+(t+1)y=t	t\frac{dy}{dt}+(t+1)y=t
derivative of x^6-4x^5+5x^4-5x^2+4x-1	\frac{d}{dx}(x^{6}-4x^{5}+5x^{4}-5x^{2}+4x-1)
integral from 1 to 5 of 4r^2ln(r)	\int\:_{1}^{5}4r^{2}\ln(r)dr
derivative of f(x)= x/(x^2-x)	derivative\:f(x)=\frac{x}{x^{2}-x}
integral of (x^3-6x-9)	\int\:(x^{3}-6x-9)dx
derivative of f(x)=(4x)/((x-9)^5)	derivative\:f(x)=\frac{4x}{(x-9)^{5}}
taylor ln(4x),1	taylor\:\ln(4x),1
integral of sqrt((2-x)/(2+x))	\int\:\sqrt{\frac{2-x}{2+x}}dx
(\partial)/(\partial x)(xy-xsin(y))	\frac{\partial\:}{\partial\:x}(xy-x\sin(y))
(((t^2+1)^{3/2})/3)^'	(\frac{(t^{2}+1)^{\frac{3}{2}}}{3})^{\prime\:}
derivative of (x+2(x-2)^3)	\frac{d}{dx}((x+2)(x-2)^{3})
derivative of-7(6x^2+7)^{-6}	derivative\:-7(6x^{2}+7)^{-6}
derivative of (c^4-x^4)/(c^4+x^4)	derivative\:\frac{c^{4}-x^{4}}{c^{4}+x^{4}}
integral of sin(x^3)x^2	\int\:\sin(x^{3})x^{2}dx
integral of (1-x)/(x^2)	\int\:\frac{1-x}{x^{2}}dx
limit as x approaches 0-of (x-1)/(x^2)	\lim\:_{x\to\:0-}(\frac{x-1}{x^{2}})
f(t)=sin(t^2)	f(t)=\sin(t^{2})
(dy)/(dx)+(7/x)y=2x+3	\frac{dy}{dx}+(\frac{7}{x})y=2x+3
derivative of (3x^2^{2x}(x^2+2x)^2)	\frac{d}{dx}((3x^{2})^{2x}(x^{2}+2x)^{2})
tangent of f(x)= x/(1+x^2),0.4,\at x=2	tangent\:f(x)=\frac{x}{1+x^{2}},0.4,\at\:x=2
limit as x approaches 0 of 1^{1/x}	\lim\:_{x\to\:0}(1^{\frac{1}{x}})
(\partial)/(\partial x)(xcos(y)+ye^x)	\frac{\partial\:}{\partial\:x}(x\cos(y)+ye^{x})
derivative of e^{2/3}	derivative\:e^{\frac{2}{3}}
integral from-pi/4 to pi/4 of 1	\int\:_{-\frac{π}{4}}^{\frac{π}{4}}1
derivative of A(2e^{-x}x-e^{-x}x^2)	\frac{d}{dx}(A(2e^{-x}x-e^{-x}x^{2}))
integral from 1 to e^3 of x^2ln(x)	\int\:_{1}^{e^{3}}x^{2}\ln(x)dx
limit as x approaches 5 of 123	\lim\:_{x\to\:5}(123)
derivative of 1/3 x^{1/2}-x^{3/2}	\frac{d}{dx}(\frac{1}{3}x^{\frac{1}{2}}-x^{\frac{3}{2}})
(-1xy^2+2y)dx+(-1x^2y+2x)dy=0	(-1xy^{2}+2y)dx+(-1x^{2}y+2x)dy=0
derivative of 4sec(θ)	derivative\:4\sec(θ)
(\partial)/(\partial x)(x^{3/2}y)	\frac{\partial\:}{\partial\:x}(x^{\frac{3}{2}}y)
derivative of (5x+6^2)	\frac{d}{dx}((5x+6)^{2})
tangent of f(x)=4sqrt(x),\at x=9	tangent\:f(x)=4\sqrt{x},\at\:x=9
5(dy)/(dx)+2x=3	5\frac{dy}{dx}+2x=3
integral of (3x^2+1)/(x^3+x)	\int\:\frac{3x^{2}+1}{x^{3}+x}dx
derivative of y=2x^{-3/4}	derivative\:y=2x^{-\frac{3}{4}}
limit as t approaches 0 of (sqrt(t^2+9-3))/(t^2)	\lim\:_{t\to\:0}(\frac{\sqrt{t^{2}+9-3}}{t^{2}})
integral of 1/(2x-1)-1/(2x-1)	\int\:\frac{1}{2x-1}-\frac{1}{2x-1}dx
xy^'=(x^3cos(2x))/y+y	xy^{\prime\:}=\frac{x^{3}\cos(2x)}{y}+y

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