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Popular Calculus Problems

limit as x approaches 0 of (4-x)/(x^2)	\lim\:_{x\to\:0}(\frac{4-x}{x^{2}})
derivative of (5^{x^3})/(4x^2)	derivative\:\frac{5^{x^{3}}}{4x^{2}}
derivative of y=ln(x-9)	derivative\:y=\ln(x-9)
integral from 0 to 1 of (2x)/(1+x^2)	\int\:_{0}^{1}\frac{2x}{1+x^{2}}dx
(d^2)/(dx^2)(2x^3-x)	\frac{d^{2}}{dx^{2}}(2x^{3}-x)
integral of 4xsqrt(4-x^2)	\int\:4x\sqrt{4-x^{2}}dx
(\partial)/(\partial x)(xy+yz+zx-3)	\frac{\partial\:}{\partial\:x}(xy+yz+zx-3)
tangent of y=e^{2x},\at x= 1/2 ln(2)	tangent\:y=e^{2x},\at\:x=\frac{1}{2}\ln(2)
limit as x approaches-1 of (\|x\|)/(x+1)	\lim\:_{x\to\:-1}(\frac{\left\|x\right\|}{x+1})
integral of xarctan(8x)	\int\:x\arctan(8x)dx
f(x)=cos^2(4x)	f(x)=\cos^{2}(4x)
derivative of (6x+e^{-x^2}^5)	\frac{d}{dx}((6x+e^{-x^{2}})^{5})
limit as x approaches 0 of (2x)/(sin(x))	\lim\:_{x\to\:0}(\frac{2x}{\sin(x)})
integral of (60x^2+20x)/(10x^3+5x^2+3)	\int\:\frac{60x^{2}+20x}{10x^{3}+5x^{2}+3}dx
derivative of y=\sqrt[x]{x}	derivative\:y=\sqrt[x]{x}
integral of 1/((x^2+64)^2)	\int\:\frac{1}{(x^{2}+64)^{2}}dx
derivative of e^{x/(10})	\frac{d}{dx}(e^{\frac{x}{10}})
limit as x approaches o-of 4	\lim\:_{x\to\:o-}(4)
derivative of (x^2+1^6)	\frac{d}{dx}((x^{2}+1)^{6})
(x^2+2xy+y^2)dx+(2xy+x^2-1)dy=0	(x^{2}+2xy+y^{2})dx+(2xy+x^{2}-1)dy=0
derivative of 30ln(3x+1)	derivative\:30\ln(3x+1)
derivative of y=(4x^2-8x+8)e^{-4x}	derivative\:y=(4x^{2}-8x+8)e^{-4x}
(\partial)/(\partial x)(ln(x+9y+8z))	\frac{\partial\:}{\partial\:x}(\ln(x+9y+8z))
(\partial)/(\partial x)(xy^2z^4)	\frac{\partial\:}{\partial\:x}(xy^{2}z^{4})
integral from 2 to 1 of-4x^{-3}	\int\:_{2}^{1}-4x^{-3}dx
integral of (x^7)/((2-x^8)^2)	\int\:\frac{x^{7}}{(2-x^{8})^{2}}dx
10000y^{''}-81y=0,y(0)=1,y^'(0)=3	10000y^{\prime\:\prime\:}-81y=0,y(0)=1,y^{\prime\:}(0)=3
(\partial)/(\partial y)((y^3)/(x^2))	\frac{\partial\:}{\partial\:y}(\frac{y^{3}}{x^{2}})
y^'=-ky^3	y^{\prime\:}=-ky^{3}
integral of (1/x+cot(x)-sec(x))	\int\:(\frac{1}{x}+\cot(x)-\sec(x))dx
derivative of e^{3x}(2sin(4x))	derivative\:e^{3\cdot\:x}\cdot\:(2\cdot\:\sin(4\cdot\:x))
integral of 1/((2y+5)^2)	\int\:\frac{1}{(2y+5)^{2}}dy
sum from n=1 to infinity of (2/3)^n	\sum\:_{n=1}^{\infty\:}(\frac{2}{3})^{n}
(dy)/(dx)=(2x+sec^2(x))/(2y)	\frac{dy}{dx}=\frac{2x+\sec^{2}(x)}{2y}
integral from-1 to 2 of 1+x^2	\int\:_{-1}^{2}1+x^{2}dx
derivative of cos(x+xsin(x))	\frac{d}{dx}(\cos(x)+x\sin(x))
xy^'-y^2=xy^2	xy^{\prime\:}-y^{2}=xy^{2}
derivative of f(x)=8sin^3(sqrt(x))	derivative\:f(x)=8\sin^{3}(\sqrt{x})
derivative of ((5x^5-3)/((-3x^3+1)))	\frac{d}{dx}(\frac{(5x^{5}-3)}{(-3x^{3}+1)})
derivative of y=2(6x^2-42x+49)	derivative\:y=2(6x^{2}-42x+49)
f(x)=25x	f(x)=25x
integral from 1 to e of 3x^2ln(x)	\int\:_{1}^{e}3x^{2}\ln(x)dx
derivative of f(x)=3x^{1/2}	derivative\:f(x)=3x^{\frac{1}{2}}
(\partial)/(\partial y)(xy-x^2y)	\frac{\partial\:}{\partial\:y}(xy-x^{2}y)
integral of 4e^{-0.8x}	\int\:4e^{-0.8x}dx
integral of x(x^2+1)^{1/2}	\int\:x(x^{2}+1)^{\frac{1}{2}}dx
(\partial)/(\partial x)(\sqrt[3]{x^2y+3y})	\frac{\partial\:}{\partial\:x}(\sqrt[3]{x^{2}y+3y})
derivative of f(x)=-3\sqrt[3]{x}	derivative\:f(x)=-3\sqrt[3]{x}
limit as x approaches+(-3)+of f(x)	\lim\:_{x\to\:+(-3)+}(f(x))
derivative of 6arctan(x)	\frac{d}{dx}(6\arctan(x))
integral of (13-13x)/(1-sqrt(x))	\int\:\frac{13-13x}{1-\sqrt{x}}dx
derivative of 2/x-1/(x^2)	\frac{d}{dx}(\frac{2}{x}-\frac{1}{x^{2}})
derivative of 2sqrt(4-y)	derivative\:2\sqrt{4-y}
integral of 1/(sqrt(x^2-a^2))	\int\:\frac{1}{\sqrt{x^{2}-a^{2}}}dx
derivative of cos(x+y)	derivative\:\cos(x+y)
integral of t/(t-1)	\int\:\frac{t}{t-1}dt
derivative of csc(5x)	\frac{d}{dx}(\csc(5x))
derivative of y=3log_{7}(x^2+1)	derivative\:y=3\log_{7}(x^{2}+1)
implicit (dy)/(dx),7x^2-280x+y^2+174=0	implicit\:\frac{dy}{dx},7x^{2}-280x+y^{2}+174=0
derivative of sin(xe^{cos(x)})	\frac{d}{dx}(\sin(x)e^{\cos(x)})
derivative of 3t^4	derivative\:3t^{4}
derivative of (2x-5(3-2x^2))	\frac{d}{dx}((2x-5)(3-2x^{2}))
tangent of y= 1/(x^2),(2, 1/4)	tangent\:y=\frac{1}{x^{2}},(2,\frac{1}{4})
(sqrt(t+1))^'	(\sqrt{t+1})^{\prime\:}
integral of 8/(x(x+2))	\int\:\frac{8}{x(x+2)}dx
limit as x approaches 0 of (sin^2(5x))/x	\lim\:_{x\to\:0}(\frac{\sin^{2}(5x)}{x})
taylor e^{-9x},0	taylor\:e^{-9x},0
laplacetransform t^2(8e^{2t}-6sin(2t))	laplacetransform\:t^{2}(8e^{2t}-6\sin(2t))
derivative of x^2-39.5x+120+(125/x)	\frac{d}{dx}(x^{2}-39.5x+120+\frac{125}{x})
limit as x approaches 0-of 1/(x^3-x)	\lim\:_{x\to\:0-}(\frac{1}{x^{3}-x})
integral of e^{-x^7}	\int\:e^{-x^{7}}dx
integral of (x+4)^5	\int\:(x+4)^{5}dx
y^'=10^{-21}y^3	y^{\prime\:}=10^{-21}y^{3}
integral of-3te^t	\int\:-3te^{t}dt
integral of ((1-x))/(x^2+1)	\int\:\frac{(1-x)}{x^{2}+1}dx
(\partial)/(\partial x)(x^{y+z})	\frac{\partial\:}{\partial\:x}(x^{y+z})
integral of x^2ln(2x-3)	\int\:x^{2}\ln(2x-3)dx
limit as x approaches-1 of x^2+5x+6	\lim\:_{x\to\:-1}(x^{2}+5x+6)
y^{''}-7y^'=-3	y^{\prime\:\prime\:}-7y^{\prime\:}=-3
limit as x approaches 0+of ln(0.1)	\lim\:_{x\to\:0+}(\ln(0.1))
(\partial)/(\partial x)(t^3e^{-(x^2)/(2t)})	\frac{\partial\:}{\partial\:x}(t^{3}e^{-\frac{x^{2}}{2t}})
derivative of 30e^{-0.0000323h}	derivative\:30e^{-0.0000323h}
integral from 0 to 7 of sqrt(4+3x)	\int\:_{0}^{7}\sqrt{4+3x}dx
inverse oflaplace s/(s^2+4s+13)	inverselaplace\:\frac{s}{s^{2}+4s+13}
limit as x approaches 4.2 of sqrt(3)	\lim\:_{x\to\:4.2}(\sqrt{3})
integral of e^{-st}sin(at)	\int\:e^{-st}\sin(at)dt
integral from-7 to 9 of (x/2+9)	\int\:_{-7}^{9}(\frac{x}{2}+9)dx
limit as x approaches 2 of x/x	\lim\:_{x\to\:2}(\frac{x}{x})
derivative of cos(2x*2)	\frac{d}{dx}(\cos(2x)\cdot\:2)
limit as x approaches 2 of x(x-2)	\lim\:_{x\to\:2}(x(x-2))
derivative of y=(x^7)/(x^5)x=0	derivative\:y=\frac{x^{7}}{x^{5}}x=0
integral of x^2cos(1/8 x)	\int\:x^{2}\cos(\frac{1}{8}x)dx
(\partial)/(\partial x)(3sin(x)sin(y))	\frac{\partial\:}{\partial\:x}(3\sin(x)\sin(y))
integral of sqrt((4-x)/(4+x))	\int\:\sqrt{\frac{4-x}{4+x}}dx
integral of (y^{2/3}-4y^{-1/5}+4)	\int\:(y^{\frac{2}{3}}-4y^{-\frac{1}{5}}+4)dy
derivative of ln((x+1/(x-3)))	\frac{d}{dx}(\ln(\frac{x+1}{x-3}))
f(x)= 5/(x^3)	f(x)=\frac{5}{x^{3}}
integral of 8u^{7/2}	\int\:8u^{\frac{7}{2}}du
taylor 5^x,0	taylor\:5^{x},0
derivative of y=(x^4+2)^2(x^5+4)^4	derivative\:y=(x^{4}+2)^{2}(x^{5}+4)^{4}

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