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Popular Calculus Problems

slope of y= 1/(x-5),\at x=10	slope\:y=\frac{1}{x-5},\at\:x=10
(1+x^2)(dy)/(dx)+4xy=(1+x^2)^{-2}	(1+x^{2})\frac{dy}{dx}+4xy=(1+x^{2})^{-2}
limit as x approaches infinity of 1-4/x	\lim\:_{x\to\:\infty\:}(1-\frac{4}{x})
integral of 5/(6e^{2x)}	\int\:\frac{5}{6e^{2x}}dx
derivative of \sqrt[3]{4-9x}	derivative\:\sqrt[3]{4-9x}
integral of (x+2)/((x+1)^2(2x-1))	\int\:\frac{x+2}{(x+1)^{2}(2x-1)}dx
integral of (sec^2(y))/(csc(y))	\int\:\frac{\sec^{2}(y)}{\csc(y)}dy
derivative of (3x/(x^2+9))	\frac{d}{dx}(\frac{3x}{x^{2}+9})
limit as x approaches 0 of x^2-2x^3	\lim\:_{x\to\:0}(x^{2}-2x^{3})
sum from n=0 to infinity of 1/(n!)x^n	\sum\:_{n=0}^{\infty\:}\frac{1}{n!}x^{n}
limit as x approaches 0 of-x^2+4x	\lim\:_{x\to\:0}(-x^{2}+4x)
y^{''}-3/x y^'+4/(x^2)y=0	y^{\prime\:\prime\:}-\frac{3}{x}y^{\prime\:}+\frac{4}{x^{2}}y=0
limit as x approaches 2 of ((\|x-2\|))/2	\lim\:_{x\to\:2}(\frac{(\left\|x-2\right\|)}{2})
derivative of 8x-5/(\sqrt[3]{x^2}+e)	\frac{d}{dx}(8x-\frac{5}{\sqrt[3]{x^{2}}}+e)
limit as x approaches 4 of sin(x-4)	\lim\:_{x\to\:4}(\sin(x-4))
derivative of tan(cos(2x))	\frac{d}{dx}(\tan(\cos(2x)))
integral of (2x)/(x^2+2x+3)	\int\:\frac{2x}{x^{2}+2x+3}dx
2x^{''}+7x^'+3x=0,x(0)=3,x^'(0)=0	2x^{\prime\:\prime\:}+7x^{\prime\:}+3x=0,x(0)=3,x^{\prime\:}(0)=0
(1+ln(x)+y/x)dx=(8-ln(x))dy	(1+\ln(x)+\frac{y}{x})dx=(8-\ln(x))dy
derivative of ln(sinh(2x))	\frac{d}{dx}(\ln(\sinh(2x)))
integral of (e^x)/(1+9e^{2x)}	\int\:\frac{e^{x}}{1+9e^{2x}}dx
limit as x approaches 3 of 2e^{x-3}	\lim\:_{x\to\:3}(2e^{x-3})
inverse oflaplace s/((s-1)^2+4)	inverselaplace\:\frac{s}{(s-1)^{2}+4}
derivative of 5^x+7^x	\frac{d}{dx}(5^{x}+7^{x})
derivative of-262144cos(2x)	\frac{d}{dx}(-262144\cos(2x))
limit as x approaches-3 of h(x)	\lim\:_{x\to\:-3}(h(x))
limit as x approaches 3 of (x^2)/(x-3)	\lim\:_{x\to\:3}(\frac{x^{2}}{x-3})
limit as x approaches 2+of \| 4/x \|	\lim\:_{x\to\:2+}(\left\|\frac{4}{x}\right\|)
integral of (12)/(1+9x^2)	\int\:\frac{12}{1+9x^{2}}dx
derivative of (4x^2+6x+2/(sqrt(x)))	\frac{d}{dx}(\frac{4x^{2}+6x+2}{\sqrt{x}})
taylor ln(x/(x+a)),1	taylor\:\ln(\frac{x}{x+a}),1
derivative of (2^x/(2^x-3^x))	\frac{d}{dx}(\frac{2^{x}}{2^{x}-3^{x}})
derivative of (2x+3/(2x))	\frac{d}{dx}(\frac{2x+3}{2x})
derivative of (sqrt(x)/(sin(x)))	\frac{d}{dx}(\frac{\sqrt{x}}{\sin(x)})
(\partial ^2)/(\partial y^2)(sin^2(mx+ny))	\frac{\partial\:^{2}}{\partial\:y^{2}}(\sin^{2}(mx+ny))
integral of (x^2)/(4x^2+9)	\int\:\frac{x^{2}}{4x^{2}+9}dx
derivative of (x+2^2)	\frac{d}{dx}((x+2)^{2})
area 3x^2,x^3	area\:3x^{2},x^{3}
(\partial)/(\partial x)(e^{7x+3y})	\frac{\partial\:}{\partial\:x}(e^{7x+3y})
integral of-xsqrt(1-x^2)	\int\:-x\sqrt{1-x^{2}}dx
derivative of-x+4	\frac{d}{dx}(-x+4)
limit as x approaches-1+of x^2	\lim\:_{x\to\:-1+}(x^{2})
d/(dt)(pi{r}(t)(t)^2h)	\frac{d}{dt}(π{r}(t)(t)^{2}h)
integral of (x+1)^2e^x	\int\:(x+1)^{2}e^{x}dx
integral of 1/(2x+4)	\int\:\frac{1}{2x+4}dx
derivative of ln(ln(x^{2x}))	\frac{d}{dx}(\ln(\ln(x^{2x})))
integral of (27)/(x(x^2+4)^2)	\int\:\frac{27}{x(x^{2}+4)^{2}}dx
(dy)/(dx)=ln(x^y)	\frac{dy}{dx}=\ln(x^{y})
integral of (x^4-4^x+\sqrt[4]{x}-4/x)	\int\:(x^{4}-4^{x}+\sqrt[4]{x}-\frac{4}{x})dx
derivative of y=((x+7))/((x-5))	derivative\:y=\frac{(x+7)}{(x-5)}
derivative of 1/2*ln(x)	\frac{d}{dx}(\frac{1}{2}\cdot\:\ln(x))
integral of r^2((r^3)/9+7)^2	\int\:r^{2}(\frac{r^{3}}{9}+7)^{2}dr
integral of (x^5)/((4-x^6)^4)	\int\:\frac{x^{5}}{(4-x^{6})^{4}}dx
derivative of 1/2 (x-1^3sin(1/(x-1)))	\frac{d}{dx}(\frac{1}{2}(x-1)^{3}\sin(\frac{1}{x-1}))
tangent of f(x)= x/(x^2+16),\at x=0	tangent\:f(x)=\frac{x}{x^{2}+16},\at\:x=0
integral of (x^2)/((15+4x-4x^2)^{3/2)}	\int\:\frac{x^{2}}{(15+4x-4x^{2})^{\frac{3}{2}}}dx
integral of (x^2e^{x^3}+x^2sin(y))	\int\:(x^{2}e^{x^{3}}+x^{2}\sin(y))dx
integral of ((x-5)/(x^2-x-6))	\int\:(\frac{x-5}{x^{2}-x-6})dx
integral of 7sin(x)	\int\:7\sin(x)dx
derivative of (x+3/(x^3+x-5))	\frac{d}{dx}(\frac{x+3}{x^{3}+x-5})
integral from 0 to 2pi of sin^2(3x)	\int\:_{0}^{2π}\sin^{2}(3x)dx
integral of x/(sqrt(5-x))	\int\:\frac{x}{\sqrt{5-x}}dx
integral of 5/(36+(x-1)^2)	\int\:\frac{5}{36+(x-1)^{2}}dx
integral of (14)/(x(x^2+4)^2)	\int\:\frac{14}{x(x^{2}+4)^{2}}dx
(ln(t^2+1))^'	(\ln(t^{2}+1))^{\prime\:}
(dy)/(dt)=y-t	\frac{dy}{dt}=y-t
tangent of y=x^4+4x^2-x	tangent\:y=x^{4}+4x^{2}-x
derivative of ln(x-8)	\frac{d}{dx}(\ln(x-8))
integral of (cos(x))/(sin^2(x)-9)	\int\:\frac{\cos(x)}{\sin^{2}(x)-9}dx
integral of (sqrt(x))/(1+x^{3/2)}	\int\:\frac{\sqrt{x}}{1+x^{\frac{3}{2}}}dx
derivative of log_{3}(2x-1)	\frac{d}{dx}(\log_{3}(2x-1))
d/(dt)(1/(t^3))	\frac{d}{dt}(\frac{1}{t^{3}})
(\partial)/(\partial x)(cos(x^2+y^2-z))	\frac{\partial\:}{\partial\:x}(\cos(x^{2}+y^{2}-z))
derivative of Be^x	\frac{d}{dx}(Be^{x})
integral of (10)/(1+e^x)	\int\:\frac{10}{1+e^{x}}dx
integral of-y^2e^y	\int\:-y^{2}e^{y}dy
integral of (1/4)^x	\int\:(\frac{1}{4})^{x}dx
limit as x approaches-3 of (1-6x)/(3+x)	\lim\:_{x\to\:-3}(\frac{1-6x}{3+x})
integral of tan(x)left(sec(x))^2	\int\:\tan(x)left(\sec(x))^{2}dx
integral of t^2sinh(t)	\int\:t^{2}\sinh(t)dt
integral from 0 to 1 of (x^2)/(x^3+1)	\int\:_{0}^{1}\frac{x^{2}}{x^{3}+1}dx
limit as x approaches 0.01 of (e^x-1)/x	\lim\:_{x\to\:0.01}(\frac{e^{x}-1}{x})
derivative of (sin(1/x x^3)/(ln(x)))	\frac{d}{dx}(\frac{\sin(\frac{1}{x})x^{3}}{\ln(x)})
area 1-x^2,x^6-x+1	area\:1-x^{2},x^{6}-x+1
limit as x approaches-infinity of x^4+x	\lim\:_{x\to\:-\infty\:}(x^{4}+x)
sin(2x)dx+cos(8y)dy=0	\sin(2x)dx+\cos(8y)dy=0
tangent of 4/3 x^3-7x+5	tangent\:\frac{4}{3}x^{3}-7x+5
integral from 0 to 2 of arctan(x/2)	\int\:_{0}^{2}\arctan(\frac{x}{2})dx
integral of (10)/(1+x^2)	\int\:\frac{10}{1+x^{2}}dx
limit as x approaches 0 of (arcsin(2x)-2arcsin(x))/(x^3)	\lim\:_{x\to\:0}(\frac{\arcsin(2x)-2\arcsin(x)}{x^{3}})
tangent of f(x)=x^2	tangent\:f(x)=x^{2}
limit as x approaches 3 of (x-2)/(x+5)	\lim\:_{x\to\:3}(\frac{x-2}{x+5})
2x^2y(dy)/(dx)+1+2xy^2=0	2x^{2}y\frac{dy}{dx}+1+2xy^{2}=0
(d^3)/(dx^3)(cot(2x)+3x^2)	\frac{d^{3}}{dx^{3}}(\cot(2x)+3x^{2})
derivative of x^4-8x^3+4x^2+48x	\frac{d}{dx}(x^{4}-8x^{3}+4x^{2}+48x)
(\partial}{\partial x}(xy+\frac{27)/x)	\frac{\partial\:}{\partial\:x}(xy+\frac{27}{x})
derivative of e^{5x+pii}	\frac{d}{dx}(e^{5x+πi})
integral of (6+x^5)^25x^4	\int\:(6+x^{5})^{2}5x^{4}dx
(\partial)/(\partial x)(-cos(2x))	\frac{\partial\:}{\partial\:x}(-\cos(2x))
(\partial)/(\partial x)(x^3+y^3-3x^2+3y^2)	\frac{\partial\:}{\partial\:x}(x^{3}+y^{3}-3x^{2}+3y^{2})

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