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Popular Calculus Problems

tangent of y=(8x)/(x^2+1)	tangent\:y=\frac{8x}{x^{2}+1}
derivative of x^{1/3}(x+3^{2/3})	\frac{d}{dx}(x^{\frac{1}{3}}(x+3)^{\frac{2}{3}})
integral of 7tan(x)	\int\:7\tan(x)dx
integral of 1/(sin^5(x)cos(x))	\int\:\frac{1}{\sin^{5}(x)\cos(x)}dx
derivative of-(x^3/3)	\frac{d}{dx}(-\frac{x^{3}}{3})
y^{''}+4y^'+4y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=0,y(0)=1,y^{\prime\:}(0)=0
integral from 1/2 to 1 of (x^{-3}-25)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-25)dx
y^{''}+1/x y^'=0	y^{\prime\:\prime\:}+\frac{1}{x}y^{\prime\:}=0
y^{''}+2x=6x^2,y(0)=3	y^{\prime\:\prime\:}+2x=6x^{2},y(0)=3
integral from-3 to 3 of pi(9-x^2)^2	\int\:_{-3}^{3}π(9-x^{2})^{2}dx
limit as x approaches 5 of (4-x)^{3/2}	\lim\:_{x\to\:5}((4-x)^{\frac{3}{2}})
integral of (8x^3)/3	\int\:\frac{8x^{3}}{3}dx
tangent of (2x-1)^2ln(2x-1),\at x=0	tangent\:(2x-1)^{2}\ln(2x-1),\at\:x=0
derivative of 3x^2cos(x^3)	\frac{d}{dx}(3x^{2}\cos(x^{3}))
(dy)/(dt)+3y=cos(2t)	\frac{dy}{dt}+3y=\cos(2t)
inverse oflaplace 1/(5s+2)	inverselaplace\:\frac{1}{5s+2}
(\partial)/(\partial x)(sin^3(x-5y))	\frac{\partial\:}{\partial\:x}(\sin^{3}(x-5y))
derivative of 30x^4-60x^3+60x-30	\frac{d}{dx}(30x^{4}-60x^{3}+60x-30)
integral of (4x^2+1)^4+(4x^2+1)^3	\int\:(4x^{2}+1)^{4}+(4x^{2}+1)^{3}dx
integral of sin(x)sin(y)	\int\:\sin(x)\sin(y)dy
area ln(x),x-2,1,2	area\:\ln(x),x-2,1,2
integral of (x^4)/(x-1)	\int\:\frac{x^{4}}{x-1}dx
inverse oflaplace 6/(s(s+2)^2(s+3))	inverselaplace\:\frac{6}{s(s+2)^{2}(s+3)}
integral of 1/(7x^4)	\int\:\frac{1}{7x^{4}}dx
integral of e^x*sin(x-pi)	\int\:e^{x}\cdot\:\sin(x-π)dx
derivative of x^4+4x^2-x	derivative\:x^{4}+4x^{2}-x
limit as x approaches-1 of f(x)g(x)	\lim\:_{x\to\:-1}(f(x)g(x))
(\partial)/(\partial x)(y^3e^{xy})	\frac{\partial\:}{\partial\:x}(y^{3}e^{xy})
derivative of f(x)=8x	derivative\:f(x)=8x
(\partial}{\partial x}(\frac{8x)/y)	\frac{\partial\:}{\partial\:x}(\frac{8x}{y})
derivative of 4e^{2t}	derivative\:4e^{2t}
integral of (x^4)	\int\:(x^{4})dx
d/(dt)(5)	\frac{d}{dt}(5)
derivative of x^2+1/(2x)	\frac{d}{dx}(x^{2}+\frac{1}{2x})
integral of 1/(ln(y))	\int\:\frac{1}{\ln(y)}dy
derivative of sqrt(8x+1)	\frac{d}{dx}(\sqrt{8x+1})
integral from 0 to 2 of (x+2)^2	\int\:_{0}^{2}(x+2)^{2}dx
f(x)=\sqrt[6]{x}	f(x)=\sqrt[6]{x}
derivative of sinh(ln(x))	\frac{d}{dx}(\sinh(\ln(x)))
limit as n approaches infinity of an^2	\lim\:_{n\to\:\infty\:}(an^{2})
derivative of y=(x^2+8x-4)(2x^{-2}+x^{-4})	derivative\:y=(x^{2}+8x-4)(2x^{-2}+x^{-4})
laplacetransform cos(4t)	laplacetransform\:\cos(4t)
limit as x approaches 1-of (x-1)/(x+1)	\lim\:_{x\to\:1-}(\frac{x-1}{x+1})
f(x)= x/(10)	f(x)=\frac{x}{10}
implicit (dy)/(dx),x=y^{10}	implicit\:\frac{dy}{dx},x=y^{10}
(\partial)/(\partial x)(-x/(1-x^2y^2))	\frac{\partial\:}{\partial\:x}(-\frac{x}{1-x^{2}y^{2}})
integral of e^xsqrt(e^x-1)	\int\:e^{x}\sqrt{e^{x}-1}dx
limit as x approaches infinity of 1/x-4	\lim\:_{x\to\:\infty\:}(\frac{1}{x}-4)
tangent of f(x)=(1+x)/(1+e^x),\at x=0	tangent\:f(x)=\frac{1+x}{1+e^{x}},\at\:x=0
inverse oflaplace (10)/(s(s+3))	inverselaplace\:\frac{10}{s(s+3)}
tangent of 2x^2-6x	tangent\:2x^{2}-6x
limit as x approaches 2+of \|x+2\|-2	\lim\:_{x\to\:2+}(\left\|x+2\right\|-2)
inverse oflaplace s/(s-3)	inverselaplace\:\frac{s}{s-3}
derivative of 4x-3ln(x)	\frac{d}{dx}(4x-3\ln(x))
limit as x approaches-2 of \|ln\|x+2\|\|	\lim\:_{x\to\:-2}(\left\|\ln\left\|x+2\right\|\right\|)
area x^2+2,-x,0,1	area\:x^{2}+2,-x,0,1
integral of (2cot(x)-3sin^2(x))/(sin(x))	\int\:\frac{2\cot(x)-3\sin^{2}(x)}{\sin(x)}dx
limit as x approaches infinity of (2170)/(1+e^{-0.156x)}	\lim\:_{x\to\:\infty\:}(\frac{2170}{1+e^{-0.156x}})
integral of 10^{5x-1}	\int\:10^{5x-1}dx
integral from 1 to infinity of 1/(11x+7)	\int\:_{1}^{\infty\:}\frac{1}{11x+7}dx
(\partial)/(\partial x)(x^8+2xy^7)	\frac{\partial\:}{\partial\:x}(x^{8}+2xy^{7})
derivative of t^4-8t^3+10^2	derivative\:t^{4}-8t^{3}+10^{2}
laplacetransform 2cos(5t)	laplacetransform\:2\cos(5t)
area y=e^x,y=e^{-x},0,4	area\:y=e^{x},y=e^{-x},0,4
derivative of (x-1)/(2-x)	derivative\:\frac{x-1}{2-x}
limit as x approaches 1+of 5-x^2	\lim\:_{x\to\:1+}(5-x^{2})
derivative of ln((e^x+e^{-x}/2))	\frac{d}{dx}(\ln(\frac{e^{x}+e^{-x}}{2}))
yy^'=-2x(1+y^2),y(0)=1	yy^{\prime\:}=-2x(1+y^{2}),y(0)=1
integral of 1.8^{0.045*x}-1	\int\:1.8^{0.045\cdot\:x}-1dx
integral of 1/(a-bx)	\int\:\frac{1}{a-bx}dx
integral of 1/(x^3sqrt(x^2-36))	\int\:\frac{1}{x^{3}\sqrt{x^{2}-36}}dx
y^'sin(5pix)=piycos(5pix)	y^{\prime\:}\sin(5πx)=πy\cos(5πx)
derivative of 2000	\frac{d}{dx}(2000)
y^{''}+4y=cos(2t)	y^{\prime\:\prime\:}+4y=\cos(2t)
integral of t(t^2+1)^3	\int\:t(t^{2}+1)^{3}dt
limit as x approaches 10 of 2^{1/(x-10)}	\lim\:_{x\to\:10}(2^{\frac{1}{x-10}})
y^'=(y^2)/(1+y^2)	y^{\prime\:}=\frac{y^{2}}{1+y^{2}}
tangent of f(x)=2x^3+3x^2-12x+4	tangent\:f(x)=2x^{3}+3x^{2}-12x+4
(\partial)/(\partial x)(cy^{-3})	\frac{\partial\:}{\partial\:x}(cy^{-3})
integral of 2-x/2	\int\:2-\frac{x}{2}dx
derivative of \sqrt[3]{x^4}	derivative\:\sqrt[3]{x^{4}}
inverse oflaplace (s-2)/((s-3)(s-1))	inverselaplace\:\frac{s-2}{(s-3)(s-1)}
tangent of f(x)= 3/(1+x^2),(1, 3/2)	tangent\:f(x)=\frac{3}{1+x^{2}},(1,\frac{3}{2})
integral of (3x^3)/(sqrt(1+x^4))	\int\:\frac{3x^{3}}{\sqrt{1+x^{4}}}dx
derivative of 5/(4+x)	\frac{d}{dx}(\frac{5}{4+x})
(\partial)/(\partial x)((e^y)/(x+y^8))	\frac{\partial\:}{\partial\:x}(\frac{e^{y}}{x+y^{8}})
area f(x)=x^2-12,g(x)=4x	area\:f(x)=x^{2}-12,g(x)=4x
derivative of (cos(x-1)/x)	\frac{d}{dx}(\frac{\cos(x)-1}{x})
y^{''}-12y+36y=0	y^{\prime\:\prime\:}-12y+36y=0
derivative of ((e^{-1-x}-e^{-1}))/x	derivative\:\frac{(e^{-1-x}-e^{-1})}{x}
integral from 1 to 3 of 5/(x^2+2x+1)	\int\:_{1}^{3}\frac{5}{x^{2}+2x+1}dx
f(x)=ln(5-x)	f(x)=\ln(5-x)
derivative of ln(x+y+5)	\frac{d}{dx}(\ln(x+y+5))
integral of 1/(200-x)	\int\:\frac{1}{200-x}dx
(dy)/(dt)+e^ty=-18e^t	\frac{dy}{dt}+e^{t}y=-18e^{t}
derivative of sqrt(4+4x)	\frac{d}{dx}(\sqrt{4+4x})
derivative of (x^2)/(sqrt(x+2))	derivative\:\frac{x^{2}}{\sqrt{x+2}}
derivative of sin^2(e^{sin^2(t)})	derivative\:\sin^{2}(e^{\sin^{2}(t)})
derivative of sqrt((x^2-1/(x^2+1)))	\frac{d}{dx}(\sqrt{\frac{x^{2}-1}{x^{2}+1}})
derivative of (6x+5^x)	\frac{d}{dx}((6x+5)^{x})

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