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Popular Calculus Problems

derivative of f(x)=(2x^2-4)-1	derivative\:f(x)=(2x^{2}-4)-1
integral of (x+sin(x))	\int\:(x+\sin(x))dx
(d^2)/(dx^2)(e^{3e^x})	\frac{d^{2}}{dx^{2}}(e^{3e^{x}})
integral of e^xtan^4(e^x)	\int\:e^{x}\tan^{4}(e^{x})dx
derivative of 6/((2-x^4))	\frac{d}{dx}(\frac{6}{(2-x)^{4}})
integral of 1/(sqrt(3x^2-2))	\int\:\frac{1}{\sqrt{3x^{2}-2}}dx
(\partial)/(\partial y)(x^2-e^{y^2})	\frac{\partial\:}{\partial\:y}(x^{2}-e^{y^{2}})
sum from n=1 to infinity of n/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{n+1}
integral of-t^3	\int\:-t^{3}dt
(\partial)/(\partial y)(-z)	\frac{\partial\:}{\partial\:y}(-z)
derivative of sin(x+1+5x)	\frac{d}{dx}(\sin(x+1)+5x)
d/(dy)(3xe^{-1/(y^3)})	\frac{d}{dy}(3xe^{-\frac{1}{y^{3}}})
(\partial)/(\partial x)(6e^x)	\frac{\partial\:}{\partial\:x}(6e^{x})
integral of tan^{-3}(x)sec^2(x)sec^2(x)	\int\:\tan^{-3}(x)\sec^{2}(x)\sec^{2}(x)dx
limit as x approaches 0 of (sin(x^8))/x	\lim\:_{x\to\:0}(\frac{\sin(x^{8})}{x})
derivative of tan(e^{7t})+e^{tan(7t)}	derivative\:\tan(e^{7t})+e^{\tan(7t)}
(\partial)/(\partial x)(y/((2sqrt(xy))))	\frac{\partial\:}{\partial\:x}(\frac{y}{(2\cdot\:\sqrt{x\cdot\:y})})
tangent of y=e^{x/3},\at x=0	tangent\:y=e^{\frac{x}{3}},\at\:x=0
integral of cos^2((2x)/3)	\int\:\cos^{2}(\frac{2x}{3})dx
sum from n=0 to infinity of 2+e^{-3n}	\sum\:_{n=0}^{\infty\:}2+e^{-3n}
inverse oflaplace g(s)= 5/(s-3)	inverselaplace\:g(s)=\frac{5}{s-3}
derivative of-2xcos(x)	\frac{d}{dx}(-2x\cos(x))
5/2 y^4y^'=(sqrt(y^5+4))/(x^3)	\frac{5}{2}y^{4}y^{\prime\:}=\frac{\sqrt{y^{5}+4}}{x^{3}}
(2x+y)dx+(x+3y)dy=0	(2x+y)dx+(x+3y)dy=0
tangent of y=4x^2-x^3,(1,3)	tangent\:y=4x^{2}-x^{3},(1,3)
area e^x,e^{2x},ln(2),ln(4)	area\:e^{x},e^{2x},\ln(2),\ln(4)
(\partial)/(\partial x)(sqrt(8-3x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{8-3x^{2}-y^{2}})
integral of (x^2+2x-6)/(x^3-x)	\int\:\frac{x^{2}+2x-6}{x^{3}-x}dx
derivative of e^{x*ln(x})	\frac{d}{dx}(e^{x\cdot\:\ln(x)})
derivative of 1/(xln^2(x))	\frac{d}{dx}(\frac{1}{x\ln^{2}(x)})
tangent of y=tan(12x^2),\at x=sqrt(pi)	tangent\:y=\tan(12x^{2}),\at\:x=\sqrt{π}
derivative of (x^2)^2	derivative\:(x^{2})^{2}
derivative of sec^2(0)	derivative\:\sec^{2}(0)
sum from n=1 to infinity of 2/(n^6)	\sum\:_{n=1}^{\infty\:}\frac{2}{n^{6}}
integral of (x^4-3x^2+4x)/(5x)	\int\:\frac{x^{4}-3x^{2}+4x}{5x}dx
limit as x approaches infinity of (e^x)/(1-e^{-x)}	\lim\:_{x\to\:\infty\:}(\frac{e^{x}}{1-e^{-x}})
limit as x approaches 1+of 3/(x^3-1)	\lim\:_{x\to\:1+}(\frac{3}{x^{3}-1})
derivative of-9e^{x^{-9}}	derivative\:-9e^{x^{-9}}
integral of 1/(x(ln(2x)))	\int\:\frac{1}{x(\ln(2x))}dx
(40cos(20t-pi/2))^'	(40\cos(20t-\frac{π}{2}))^{\prime\:}
integral of te^{-7t}	\int\:te^{-7t}dt
limit as x approaches 2 of (2x)/(x^2-4)	\lim\:_{x\to\:2}(\frac{2x}{x^{2}-4})
integral of 1/(4+3x)	\int\:\frac{1}{4+3x}dx
(dy)/(dx)=e^{y+2x}	\frac{dy}{dx}=e^{y+2x}
y^{''}+y^'=2e^x+14	y^{\prime\:\prime\:}+y^{\prime\:}=2e^{x}+14
integral of 8x-2x^2	\int\:8x-2x^{2}dx
(\partial)/(\partial y)(cos(xy)-e^z+2)	\frac{\partial\:}{\partial\:y}(\cos(xy)-e^{z}+2)
(\partial)/(\partial y)(rcos(y))	\frac{\partial\:}{\partial\:y}(r\cos(y))
derivative of 4x^2-5x+4	\frac{d}{dx}(4x^{2}-5x+4)
derivative of f(x)=x^{4cos(x)}	derivative\:f(x)=x^{4\cos(x)}
limit as n approaches infinity of-10^n	\lim\:_{n\to\:\infty\:}(-10^{n})
limit as x approaches-3 of x/(x+5)	\lim\:_{x\to\:-3}(\frac{x}{x+5})
derivative of (x^2-3^3)	\frac{d}{dx}((x^{2}-3)^{3})
integral of (14)/((1-x^2)^{3/2)}	\int\:\frac{14}{(1-x^{2})^{\frac{3}{2}}}dx
integral of ln(x^6)	\int\:\ln(x^{6})dx
(dy)/(dt)=(3(y+1))/(t^2+5t+6)	\frac{dy}{dt}=\frac{3(y+1)}{t^{2}+5t+6}
derivative of 1/(\sqrt[3]{x^2+x+1})	\frac{d}{dx}(\frac{1}{\sqrt[3]{x^{2}+x+1}})
(dy)/(dx)=(x^4y^4+4x^4)/(y^3)	\frac{dy}{dx}=\frac{x^{4}y^{4}+4x^{4}}{y^{3}}
integral of 1/(x^3sqrt(4x^2-9))	\int\:\frac{1}{x^{3}\sqrt{4x^{2}-9}}dx
integral of csc^2(6θ)cot(6θ)	\int\:\csc^{2}(6θ)\cot(6θ)dθ
limit as x approaches infinity of x*x	\lim\:_{x\to\:\infty\:}(x\cdot\:x)
limit as x approaches 0 of (sin(15x))/x	\lim\:_{x\to\:0}(\frac{\sin(15x)}{x})
integral of e^{-0.1x}	\int\:e^{-0.1x}dx
tangent of x^3+y^3=9,(1,2)	tangent\:x^{3}+y^{3}=9,(1,2)
integral of sqrt((a^2-x^2))	\int\:\sqrt{(a^{2}-x^{2})}dx
derivative of (ln(x)/(x^{3/2)})	\frac{d}{dx}(\frac{\ln(x)}{x^{\frac{3}{2}}})
limit as x approaches 0-of 3-4/x	\lim\:_{x\to\:0-}(3-\frac{4}{x})
taylor x^3,-1	taylor\:x^{3},-1
integral of (e^{2x})/(5+e^x)	\int\:\frac{e^{2x}}{5+e^{x}}dx
f(x)=ln(x)-1/x	f(x)=\ln(x)-\frac{1}{x}
derivative of x^3(1-x)^{100}+x^4-5pi	derivative\:x^{3}(1-x)^{100}+x^{4}-5π
derivative of 3x^3-64x	\frac{d}{dx}(3x^{3}-64x)
limit as x approaches 1+of tan((pix)/2)	\lim\:_{x\to\:1+}(\tan(\frac{πx}{2}))
limit as x approaches 1/2 of x	\lim\:_{x\to\:\frac{1}{2}}(x)
derivative of-x*ln(x)	\frac{d}{dx}(-x\cdot\:\ln(x))
limit as x approaches 0 of (2.8^x-1)/x	\lim\:_{x\to\:0}(\frac{2.8^{x}-1}{x})
integral of 1/(2u)	\int\:\frac{1}{2u}du
121y^{''}+198y^'+65y=0	121y^{\prime\:\prime\:}+198y^{\prime\:}+65y=0
derivative of (x^2-6x+8)^4	derivative\:(x^{2}-6x+8)^{4}
(1+ln(x)+y/x)dx=(1-ln(x))dy	(1+\ln(x)+\frac{y}{x})dx=(1-\ln(x))dy
derivative of 7-4e^{-x}	\frac{d}{dx}(7-4e^{-x})
(-(q^4)/4+(2q^3)/3+(11q^2)/2-12q)^'	(-\frac{q^{4}}{4}+\frac{2q^{3}}{3}+\frac{11q^{2}}{2}-12q)^{\prime\:}
3e^{6x}(dy)/(dx)=-36 x/(y^2)	3e^{6x}\frac{dy}{dx}=-36\frac{x}{y^{2}}
integral from 1/5 to 7 of 6xln(5x)	\int\:_{\frac{1}{5}}^{7}6x\ln(5x)dx
derivative of f(x)=(x^2-9)^2	derivative\:f(x)=(x^{2}-9)^{2}
(dy)/(dx)=(3y^2cot(x)+sin(x)cos(x))/(2y)	\frac{dy}{dx}=\frac{3y^{2}\cot(x)+\sin(x)\cos(x)}{2y}
limit as x approaches 10 of 8/((x-10)^2)	\lim\:_{x\to\:10}(\frac{8}{(x-10)^{2}})
derivative of (2x+1/(2x-1))	\frac{d}{dx}(\frac{2x+1}{2x-1})
(10xe^x-5xy)dx+(2xy-5x^2)dy=0	(10xe^{x}-5xy)dx+(2xy-5x^{2})dy=0
x^2y^{''}-2y=3x^2-1	x^{2}y^{\prime\:\prime\:}-2y=3x^{2}-1
derivative of y=ln(2-9x)	derivative\:y=\ln(2-9x)
derivative of cos(3x^5+1)	\frac{d}{dx}(\cos(3x^{5}+1))
limit as x approaches infinity of x^2+y	\lim\:_{x\to\:\infty\:}(x^{2}+y)
xy^'+3y=(e^x)/x	xy^{\prime\:}+3y=\frac{e^{x}}{x}
integral of 1/((x^2-36)^2)	\int\:\frac{1}{(x^{2}-36)^{2}}dx
integral of xsin(3x+2)	\int\:x\sin(3x+2)dx
derivative of e^{(x-1^2})	\frac{d}{dx}(e^{(x-1)^{2}})
integral of ((e^{2x}))/(25+e^{4x)}	\int\:\frac{(e^{2x})}{25+e^{4x}}dx
integral of e^xsqrt(7+e^x)	\int\:e^{x}\sqrt{7+e^{x}}dx
integral of-1/262144 cos(8x)	\int\:-\frac{1}{262144}\cos(8x)dx

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