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Popular Calculus Problems

integral of 1/(\sqrt[3]{y)}	\int\:\frac{1}{\sqrt[3]{y}}dy
derivative of f(x)=(-16x^2+1)^2	derivative\:f(x)=(-16x^{2}+1)^{2}
integral of 4x^2+9	\int\:4x^{2}+9dx
integral of 2(1-1/(x^2))	\int\:2(1-\frac{1}{x^{2}})dx
integral of (e^x-15^x)	\int\:(e^{x}-15^{x})dx
(\partial)/(\partial x)(x^3+x^2y)	\frac{\partial\:}{\partial\:x}(x^{3}+x^{2}y)
integral of (cos(3x))/(1+sin^2(3x))	\int\:\frac{\cos(3x)}{1+\sin^{2}(3x)}dx
limit as x approaches 0 of tan(2x)	\lim\:_{x\to\:0}(\tan(2x))
derivative of 3x+9	\frac{d}{dx}(3x+9)
(\partial)/(\partial y)(e^{ax+y}+e^y)	\frac{\partial\:}{\partial\:y}(e^{ax+y}+e^{y})
derivative of a^{(1/2)}(7x-a)+2a	derivative\:a^{(\frac{1}{2})}(7x-a)+2a
slope of x-x^3	slope\:x-x^{3}
tangent of x^{1/3+y^{1/3}}=7	tangent\:x^{\frac{1}{3}+y^{\frac{1}{3}}}=7
y^{''}-2y^'+17y=0	y^{\prime\:\prime\:}-2y^{\prime\:}+17y=0
limit as x approaches 1 of (-1)/x	\lim\:_{x\to\:1}(\frac{-1}{x})
limit as x approaches 0+of (x+1)^{In(x)}	\lim\:_{x\to\:0+}((x+1)^{In(x)})
derivative of-5sin(x(sqrt(x)+3sin(x)))	\frac{d}{dx}(-5\sin(x)(\sqrt{x}+3\sin(x)))
derivative of (x^9-2)^3	derivative\:(x^{9}-2)^{3}
limit as x approaches 1 of 2-x	\lim\:_{x\to\:1}(2-x)
(\partial)/(\partial x)((2xy)/((x^2-y^2)^2))	\frac{\partial\:}{\partial\:x}(\frac{2xy}{(x^{2}-y^{2})^{2}})
y^'-3/x y=4x^3cos(2x)	y^{\prime\:}-\frac{3}{x}y=4x^{3}\cos(2x)
derivative of f(x)=x^{1/3}	derivative\:f(x)=x^{\frac{1}{3}}
(x+1)(dy)/(dx)=x	(x+1)\frac{dy}{dx}=x
laplacetransform 3t^2+3t-2	laplacetransform\:3t^{2}+3t-2
integral of (ln(3x))/(x^3)	\int\:\frac{\ln(3x)}{x^{3}}dx
slope of (0.2)(4.3)	slope\:(0.2)(4.3)
integral of 2x-3e^x	\int\:2x-3e^{x}dx
derivative of 2x^2+5x+18	\frac{d}{dx}(2x^{2}+5x+18)
limit as t approaches 0 of (8^t-5^t)/t	\lim\:_{t\to\:0}(\frac{8^{t}-5^{t}}{t})
integral of (y^2)/(y+1)	\int\:\frac{y^{2}}{y+1}dy
(\partial)/(\partial u)(vsin(u))	\frac{\partial\:}{\partial\:u}(v\sin(u))
derivative of sqrt(2)sec(x)	\frac{d}{dx}(\sqrt{2}\sec(x))
derivative of (3-8x/(x+4))	\frac{d}{dx}(\frac{3-8x}{x+4})
derivative of-(10)/(\sqrt[4]{x)}	derivative\:-\frac{10}{\sqrt[4]{x}}
inverse oflaplace (s^3+s+6)/(s^4(s+2))	inverselaplace\:\frac{s^{3}+s+6}{s^{4}(s+2)}
integral from 7 to 8 of x/(x^2-3)	\int\:_{7}^{8}\frac{x}{x^{2}-3}dx
limit as x approaches 7+of 3x+5	\lim\:_{x\to\:7+}(3x+5)
derivative of sqrt(x)	derivative\:\sqrt{x}
(dy)/(dt)=2y-3e^{-t}	\frac{dy}{dt}=2y-3e^{-t}
tangent of f(x)=x^3-2x+2,\at x=2	tangent\:f(x)=x^{3}-2x+2,\at\:x=2
limit as x approaches 0-of-2x^2+7x	\lim\:_{x\to\:0-}(-2x^{2}+7x)
tangent of y=x^4+6x^2-x,(1,6)	tangent\:y=x^{4}+6x^{2}-x,(1,6)
(\partial)/(\partial y)(y^x-ln(x^4y+7x))	\frac{\partial\:}{\partial\:y}(y^{x}-\ln(x^{4}y+7x))
inverse oflaplace ((2s+3))/(s^2+2s+26)	inverselaplace\:\frac{(2s+3)}{s^{2}+2s+26}
integral of (6x)/(1-7x^2)	\int\:\frac{6x}{1-7x^{2}}dx
2xy^'+y=10sqrt(x)	2xy^{\prime\:}+y=10\sqrt{x}
derivative of (2(-x^2+1)/((x^2+1)^2))	\frac{d}{dx}(\frac{2(-x^{2}+1)}{(x^{2}+1)^{2}})
derivative of \sqrt[3]{t^2}+6sqrt(t^3)	derivative\:\sqrt[3]{t^{2}}+6\sqrt{t^{3}}
integral of (x^3+1)^3	\int\:(x^{3}+1)^{3}dx
derivative of f(x)= 8/(7x^2)	derivative\:f(x)=\frac{8}{7x^{2}}
tangent of f(x)=x^2-2x+1	tangent\:f(x)=x^{2}-2x+1
derivative of (2x^2-4x^{-2})	\frac{d}{dx}((2x^{2}-4x)^{-2})
limit as x approaches infinity of (x)^2	\lim\:_{x\to\:\infty\:}((x)^{2})
sum from k=0 to infinity of (3^k)/(k!)	\sum\:_{k=0}^{\infty\:}\frac{3^{k}}{k!}
derivative of (x^2-3x+11)/(x^2+x-3)	derivative\:\frac{x^{2}-3x+11}{x^{2}+x-3}
(\partial)/(\partial θ)(cos(θ))	\frac{\partial\:}{\partial\:θ}(\cos(θ))
limit as x approaches 0 of x/2	\lim\:_{x\to\:0}(\frac{x}{2})
derivative of f(x)=e^{x+1}	derivative\:f(x)=e^{x+1}
derivative of x^{1/3}+(x-4)/(3x^{5/3)}	derivative\:x^{\frac{1}{3}}+\frac{x-4}{3x^{\frac{5}{3}}}
derivative of-sin(x^2+3*2x)	\frac{d}{dx}(-\sin(x^{2}+3)\cdot\:2x)
integral of 5x^2(2x^3+3)^4	\int\:5x^{2}(2x^{3}+3)^{4}dx
derivative of-13x^pi+2+\sqrt[4]{x^3}	\frac{d}{dx}(-13x^{π}+2+\sqrt[4]{x^{3}})
integral of ((ln(ln(x))))/x	\int\:\frac{(\ln(\ln(x)))}{x}dx
(\partial)/(\partial y)(ye^{-x})	\frac{\partial\:}{\partial\:y}(ye^{-x})
limit as x approaches-2 of x^2+5x+7	\lim\:_{x\to\:-2}(x^{2}+5x+7)
taylor 1/(x^2),5	taylor\:\frac{1}{x^{2}},5
derivative of-1/4 x^2	\frac{d}{dx}(-\frac{1}{4}x^{2})
tangent of f(x)= 1/x ,\at x=0.204	tangent\:f(x)=\frac{1}{x},\at\:x=0.204
integral of (u^2-1)/(u^2+1)	\int\:\frac{u^{2}-1}{u^{2}+1}du
tangent of f(x)=5e^x,\at x=3	tangent\:f(x)=5e^{x},\at\:x=3
(dy)/(dx)=(sin(2x))/(e^y)	\frac{dy}{dx}=\frac{\sin(2x)}{e^{y}}
derivative of (x^3/((x+2)^2))	\frac{d}{dx}(\frac{x^{3}}{(x+2)^{2}})
integral of 36(4x+4)^{(2)}-2sqrt((3x-1))	\int\:36(4x+4)^{(2)}-2\sqrt{(3x-1)}dx
integral of cos^{-1}(x)	\int\:\cos^{-1}(x)dx
tangent of x^2+9	tangent\:x^{2}+9
integral from 1 to 5 of (x^2+8)/(6x-x^2)	\int\:_{1}^{5}\frac{x^{2}+8}{6x-x^{2}}dx
derivative of ((x+1^2)/(x^2+1))	\frac{d}{dx}(\frac{(x+1)^{2}}{x^{2}+1})
integral of (cot^2(x))/(cos^2(x))	\int\:\frac{\cot^{2}(x)}{\cos^{2}(x)}dx
derivative of 1/4 (e^{2x}+e^{-2x})	\frac{d}{dx}(\frac{1}{4}(e^{2x}+e^{-2x}))
derivative of (x^3-x^2+1/5)	\frac{d}{dx}(\frac{x^{3}-x^{2}+1}{5})
integral of 2/(sqrt(1+e^{2x))}	\int\:\frac{2}{\sqrt{1+e^{2x}}}dx
(cos^2(x)-2sin(x))^'	(\cos^{2}(x)-2\sin(x))^{\prime\:}
integral of (sec^2(x))/(sqrt(1+2tan(x)))	\int\:\frac{\sec^{2}(x)}{\sqrt{1+2\tan(x)}}dx
integral of ((3x^2-2))/(x(x+1)^3)	\int\:\frac{(3x^{2}-2)}{x(x+1)^{3}}dx
integral of (5x^4+64)arctan(x/2)	\int\:(5x^{4}+64)\arctan(\frac{x}{2})dx
derivative of f(x)=sqrt(5-x)	derivative\:f(x)=\sqrt{5-x}
simplify log_{10}(((x+1)(x-8))/((x-1)(x+8)))	simplify\:\log_{10}(\frac{(x+1)(x-8)}{(x-1)(x+8)})
sum from n=1 to infinity of 1/(5^{n+1)}	\sum\:_{n=1}^{\infty\:}\frac{1}{5^{n+1}}
integral of 3^x+2/x	\int\:3^{x}+\frac{2}{x}dx
(\partial)/(\partial x)(e^{8xy})	\frac{\partial\:}{\partial\:x}(e^{8xy})
limit as n approaches infinity of 1/(log_{2)(n)}	\lim\:_{n\to\:\infty\:}(\frac{1}{\log_{2}(n)})
derivative of x^k	\frac{d}{dx}(x^{k})
limit as x approaches infinity of-1/3	\lim\:_{x\to\:\infty\:}(-\frac{1}{3})
integral of (x+arcsin(x))/(sqrt(1-x^2))	\int\:\frac{x+\arcsin(x)}{\sqrt{1-x^{2}}}dx
derivative of ((x^2)/(2+x))	\frac{d}{dx}(\frac{(x^{2})}{2+x})
slope of 1/(x-4)	slope\:\frac{1}{x-4}
limit as x approaches 1+of 2/x-1/(ln(x))	\lim\:_{x\to\:1+}(\frac{2}{x}-\frac{1}{\ln(x)})
(\partial)/(\partial x)(2y*arctan(x/y))	\frac{\partial\:}{\partial\:x}(2y\cdot\:\arctan(\frac{x}{y}))
derivative of 6x+4	derivative\:6x+4
derivative of x^2+4/(x^2)	\frac{d}{dx}(x^{2}+\frac{4}{x^{2}})

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