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Popular Calculus Problems

derivative of (2x+1/(x+2))	\frac{d}{dx}(\frac{2x+1}{x+2})
derivative of ln((7+e^x/(7-e^x)))	\frac{d}{dx}(\ln(\frac{7+e^{x}}{7-e^{x}}))
integral from 0 to 5 of 1/(x^{13/12)}	\int\:_{0}^{5}\frac{1}{x^{\frac{13}{12}}}dx
derivative of \sqrt[3]{tan^2(x})	\frac{d}{dx}(\sqrt[3]{\tan^{2}(x)})
derivative of log_{n}(x)	\frac{d}{dx}(\log_{n}(x))
t^2(dy)/(dt)+y^2=ty	t^{2}\frac{dy}{dt}+y^{2}=ty
integral of x(1-2x)	\int\:x(1-2x)dx
derivative of (3x^2+2sqrt(x)/x)	\frac{d}{dx}(\frac{3x^{2}+2\sqrt{x}}{x})
derivative of cot(xcsc(x))	\frac{d}{dx}(\cot(x)\csc(x))
derivative of g(x)=e^{x^2-x}	derivative\:g(x)=e^{x^{2}-x}
derivative of-2x+6	\frac{d}{dx}(-2x+6)
integral of 8/(xln(5x))	\int\:\frac{8}{x\ln(5x)}dx
sum from n=1 to infinity of 1/(3n-1)	\sum\:_{n=1}^{\infty\:}\frac{1}{3n-1}
integral of 1/(x^2sqrt(x^2-225))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-225}}dx
derivative of cot(9x)	\frac{d}{dx}(\cot(9x))
derivative of f(x)=-9cos(3x)	derivative\:f(x)=-9\cos(3x)
implicit (dy)/(dx),ln(x^2+y^2)=2(arctan(y/x))	implicit\:\frac{dy}{dx},\ln(x^{2}+y^{2})=2(\arctan(\frac{y}{x}))
slope of (0,15),(6,0)	slope\:(0,15),(6,0)
limit as x approaches 0 of 7sec^2(7x)	\lim\:_{x\to\:0}(7\sec^{2}(7x))
integral of (\sqrt[3]{t^2}-sin(t))	\int\:(\sqrt[3]{t^{2}}-\sin(t))dt
(\partial)/(\partial x)(100x^{0.66}y^{0.34})	\frac{\partial\:}{\partial\:x}(100x^{0.66}y^{0.34})
derivative of a^{3x^2}	\frac{d}{dx}(a^{3x^{2}})
taylor-4x^3+3x^2-6x+10	taylor\:-4x^{3}+3x^{2}-6x+10
derivative of y=x^3-14x^2+32x+4	derivative\:y=x^{3}-14x^{2}+32x+4
limit as s approaches 0 of (-2s)/(s-3)	\lim\:_{s\to\:0}(\frac{-2s}{s-3})
area y=-x^2+4,y=1-x	area\:y=-x^{2}+4,y=1-x
integral from 1 to 6 of (sqrt(x^2-1))/x	\int\:_{1}^{6}\frac{\sqrt{x^{2}-1}}{x}dx
y^{''}-2y^'+2y=2x-2,y(0)=0,y(pi)=pi	y^{\prime\:\prime\:}-2y^{\prime\:}+2y=2x-2,y(0)=0,y(π)=π
integral of 3x^3cos(x^2)	\int\:3x^{3}\cos(x^{2})dx
integral of ((5x+3))/((x^3-2x^2-3x))	\int\:\frac{(5x+3)}{(x^{3}-2x^{2}-3x)}dx
tangent of x^2+y^2=169,(-5,12)	tangent\:x^{2}+y^{2}=169,(-5,12)
laplacetransform 1-2t	laplacetransform\:1-2t
limit as x approaches infinity of pix	\lim\:_{x\to\:\infty\:}(πx)
derivative of \sqrt[7]{t}+2sqrt(t^7)	derivative\:\sqrt[7]{t}+2\sqrt{t^{7}}
derivative of x{f}(x+{f}(x)(cx)+c{f}(x))	\frac{d}{dx}(x{f}(x)+{f}(x)(cx)+c{f}(x))
integral from 1 to 2 of-x+85/50	\int\:_{1}^{2}-x+\frac{85}{50}dx
integral of tan^2(x)*sec^3(x)	\int\:\tan^{2}(x)\cdot\:\sec^{3}(x)dx
(\partial)/(\partial x)(ln(x+4y+9z))	\frac{\partial\:}{\partial\:x}(\ln(x+4y+9z))
tangent of y=6x-x^2,(1,5)	tangent\:y=6x-x^{2},(1,5)
integral of (x+2)/(sqrt(x^2+9))	\int\:\frac{x+2}{\sqrt{x^{2}+9}}dx
integral of 6/(x-5)	\int\:\frac{6}{x-5}dx
(\partial)/(\partial y)(3x^2y)	\frac{\partial\:}{\partial\:y}(3x^{2}y)
integral from 0 to 12 of sqrt(1+x/4)	\int\:_{0}^{12}\sqrt{1+\frac{x}{4}}dx
tangent of y=14(sin(x)+cos(x))	tangent\:y=14(\sin(x)+\cos(x))
sum from n=0 to infinity of e^{3-2n}	\sum\:_{n=0}^{\infty\:}e^{3-2n}
limit as x approaches 0 of (a^{2x}-1)/x	\lim\:_{x\to\:0}(\frac{a^{2x}-1}{x})
limit as x approaches 7 of 1/(x^2(x+7))	\lim\:_{x\to\:7}(\frac{1}{x^{2}(x+7)})
derivative of asqrt(cos(2x))	\frac{d}{dx}(a\sqrt{\cos(2x)})
integral of x/(sqrt(x^2+8x))	\int\:\frac{x}{\sqrt{x^{2}+8x}}dx
tangent of y=ax^3	tangent\:y=ax^{3}
integral from 0 to 1 of (ln(t))/t	\int\:_{0}^{1}\frac{\ln(t)}{t}dt
integral of+x^3e^{3x^2}	\int\:+x^{3}e^{3x^{2}}dx
limit as x approaches 1+of (x^2-4)/(x-1)	\lim\:_{x\to\:1+}(\frac{x^{2}-4}{x-1})
integral of (20000)/((x+100)^3)	\int\:\frac{20000}{(x+100)^{3}}dx
integral of 8xe^{x^2}	\int\:8xe^{x^{2}}dx
integral of (-1)	\int\:(-1)dx
(\partial}{\partial z}(\frac{xy)/z)	\frac{\partial\:}{\partial\:z}(\frac{xy}{z})
(\partial)/(\partial x)(7-x^4+2x^2-y^2)	\frac{\partial\:}{\partial\:x}(7-x^{4}+2x^{2}-y^{2})
(dy)/(dx)+5y=e^xy^{-2}	\frac{dy}{dx}+5y=e^{x}y^{-2}
derivative of (x^2-2sin(x)+2xcos(x))	\frac{d}{dx}((x^{2}-2)\sin(x)+2x\cos(x))
limit as x approaches 2 of (\|x-3\|)/(x-3)	\lim\:_{x\to\:2}(\frac{\left\|x-3\right\|}{x-3})
integral of tan^3(5x)sec^2(5x)	\int\:\tan^{3}(5x)\sec^{2}(5x)dx
derivative of (1+cos(x)/(1-cos(x)))	\frac{d}{dx}(\frac{1+\cos(x)}{1-\cos(x)})
derivative of (sin(x)/(1-cos(x)))	\frac{d}{dx}(\frac{\sin(x)}{1-\cos(x)})
d/(dθ)(sin(θ))	\frac{d}{dθ}(\sin(θ))
limit as x approaches-5 of ((x-5))/(x+5)	\lim\:_{x\to\:-5}(\frac{(x-5)}{x+5})
laplacetransform 8t^4	laplacetransform\:8t^{4}
integral of ((x+4))/(x^2+8x+17)	\int\:\frac{(x+4)}{x^{2}+8x+17}dx
y^'+2/t y=(cos(t))/(t^2),y(pi)=0	y^{\prime\:}+\frac{2}{t}y=\frac{\cos(t)}{t^{2}},y(π)=0
derivative of 2/(\sqrt[3]{x-1})	\frac{d}{dx}(\frac{2}{\sqrt[3]{x-1}})
simplify 1/(sqrt(3x+5))	simplify\:\frac{1}{\sqrt{3x+5}}
integral of-25cos(-5t)	\int\:-25\cos(-5t)dt
limit as x approaches-1 of 2/(x+1)	\lim\:_{x\to\:-1}(\frac{2}{x+1})
derivative of 2^{t^3}	derivative\:2^{t^{3}}
derivative of (x^2-2x/(x^2+5x))	\frac{d}{dx}(\frac{x^{2}-2x}{x^{2}+5x})
integral of 1/(xsqrt(25x^2-1))	\int\:\frac{1}{x\sqrt{25x^{2}-1}}dx
x^2(dy)/(dx)-ysqrt(x)=0	x^{2}\frac{dy}{dx}-y\sqrt{x}=0
sum from n=0 to infinity of e^{-2n}	\sum\:_{n=0}^{\infty\:}e^{-2n}
limit as x approaches-4-of sqrt(5x+20)-8	\lim\:_{x\to\:-4-}(\sqrt{5x+20}-8)
(e^y+1)^2e^{-y}dx+(e^x+1)^3e^{-x}dy=0	(e^{y}+1)^{2}e^{-y}dx+(e^{x}+1)^{3}e^{-x}dy=0
(\partial)/(\partial y)(x+e^z+y)	\frac{\partial\:}{\partial\:y}(x+e^{z}+y)
tangent of (sqrt(x))/(x+4),\at 1,0.2	tangent\:\frac{\sqrt{x}}{x+4},\at\:1,0.2
tangent of sqrt(3x+4),\at x=7	tangent\:\sqrt{3x+4},\at\:x=7
limit as x approaches 0-of xln(-x)	\lim\:_{x\to\:0-}(x\ln(-x))
derivative of x+sin^2(x/3-8)	\frac{d}{dx}(x+\sin^{2}(\frac{x}{3})-8)
derivative of-3^x	\frac{d}{dx}(-3^{x})
integral from 0 to pi of sin^6(x)	\int\:_{0}^{π}\sin^{6}(x)dx
2y^{''}-2y^'+y=0	2y^{\prime\:\prime\:}-2y^{\prime\:}+y=0
integral of 1/(sqrt(t))	\int\:\frac{1}{\sqrt{t}}dt
derivative of-1/((x+4^2))	\frac{d}{dx}(-\frac{1}{(x+4)^{2}})
derivative of f(x)=4(x^2+4x)^3	derivative\:f(x)=4(x^{2}+4x)^{3}
y^'=-y^3	y^{\prime\:}=-y^{3}
derivative of sqrt(5+tan^2(x))	\frac{d}{dx}(\sqrt{5+\tan^{2}(x)})
(\partial)/(\partial y)(y^6sin(4x))	\frac{\partial\:}{\partial\:y}(y^{6}\sin(4x))
integral from 0 to 1 of sqrt(1+x)	\int\:_{0}^{1}\sqrt{1+x}dx
integral from 0 to 1 of pi(1-x^2)^2	\int\:_{0}^{1}π(1-x^{2})^{2}dx
(3+4x)+(5y-1)(dy)/(dx)=0	(3+4x)+(5y-1)\frac{dy}{dx}=0
tangent of f(x)=x^2+5x-2,\at x=4	tangent\:f(x)=x^{2}+5x-2,\at\:x=4
limit as x approaches 0 of 2x^2+3x	\lim\:_{x\to\:0}(2x^{2}+3x)
integral of (1+4x)/(sqrt(1+x+2x^2))	\int\:\frac{1+4x}{\sqrt{1+x+2x^{2}}}dx

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