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Popular Calculus Problems

derivative of (xcos(x)-sin(x))/(7x^2)	derivative\:\frac{x\cos(x)-\sin(x)}{7x^{2}}
derivative of x^3-6x^2+9x+4	\frac{d}{dx}(x^{3}-6x^{2}+9x+4)
integral from 0 to 5 of 1/(u^2-25)	\int\:_{0}^{5}\frac{1}{u^{2}-25}du
tangent of y=4cos(x),(pi/3 ,2)	tangent\:y=4\cos(x),(\frac{π}{3},2)
derivative of \sqrt[8]{x}-7/x	\frac{d}{dx}(\sqrt[8]{x}-\frac{7}{x})
derivative of-x^{-2}e^{1/x}	derivative\:-x^{-2}e^{\frac{1}{x}}
tangent of 5+4x^2-2x^3	tangent\:5+4x^{2}-2x^{3}
derivative of x/8-8/x	derivative\:\frac{x}{8}-\frac{8}{x}
y^{''}-7y^'+6y=0	y^{\prime\:\prime\:}-7y^{\prime\:}+6y=0
integral of (y^3)/(y^2+1)	\int\:\frac{y^{3}}{y^{2}+1}dy
derivative of axcos(3x+bxsin(3x))	\frac{d}{dx}(ax\cos(3x)+bx\sin(3x))
integral of 2/(t^2)	\int\:\frac{2}{t^{2}}dt
integral of (x^3-sin(x))	\int\:(x^{3}-\sin(x))dx
integral of 1/(cos^2(5x))	\int\:\frac{1}{\cos^{2}(5x)}dx
limit as x approaches 1 of (2*x+3)/(x+4)	\lim\:_{x\to\:1}(\frac{2\cdot\:x+3}{x+4})
integral of (x+1)/(sqrt(3-2x-x^2))	\int\:\frac{x+1}{\sqrt{3-2x-x^{2}}}dx
(\partial)/(\partial y)(e^{xy}tan(y))	\frac{\partial\:}{\partial\:y}(e^{xy}\tan(y))
derivative of 1+(5e^{-2x^2}/(2-\|x\|))	\frac{d}{dx}(1+\frac{5e^{-2x^{2}}}{2-\left\|x\right\|})
derivative of y=cos(sqrt(sin(tan(7x))))	derivative\:y=\cos(\sqrt{\sin(\tan(7x))})
integral from 0 to 8 of 1/((8-x))	\int\:_{0}^{8}\frac{1}{(8-x)}dx
integral of 2e^{-0.8x}	\int\:2e^{-0.8x}dx
xy^'+3x-2y=0	xy^{\prime\:}+3x-2y=0
e^{2x}y^'+2e^{2x}y=2x	e^{2x}y^{\prime\:}+2e^{2x}y=2x
derivative of e^{-x^2}(1-2x^2)	derivative\:e^{-x^{2}}(1-2x^{2})
limit as x approaches 6+of x^3+cx	\lim\:_{x\to\:6+}(x^{3}+cx)
derivative of f(x)=x+xsqrt(x)	derivative\:f(x)=x+x\sqrt{x}
taylor ln(x),3	taylor\:\ln(x),3
limit as x approaches 6 of h(x)	\lim\:_{x\to\:6}(h(x))
inverse oflaplace 1/((s+2)^2)	inverselaplace\:\frac{1}{(s+2)^{2}}
(dy)/(dx)=sqrt(yx)	\frac{dy}{dx}=\sqrt{yx}
integral from 0 to 3 of 2pi(x)(3x-x^2)	\int\:_{0}^{3}2π(x)(3x-x^{2})dx
limit as x approaches infinity of ((3n-7)^{2n-1})/((3n-4)^{2n+1)}	\lim\:_{x\to\:\infty\:}(\frac{(3n-7)^{2n-1}}{(3n-4)^{2n+1}})
derivative of 2/3 (4y^2+1/2)^{3/2}	derivative\:\frac{2}{3}(4y^{2}+\frac{1}{2})^{\frac{3}{2}}
(\partial)/(\partial y)(6x^2y)	\frac{\partial\:}{\partial\:y}(6x^{2}y)
derivative of 1/3 x^{3/2}-x^5+pi^4	\frac{d}{dx}(\frac{1}{3}x^{\frac{3}{2}}-x^{5}+π^{4})
d/(dt)(sqrt(2t))	\frac{d}{dt}(\sqrt{2t})
25y^{''}-y=(xex)/5	25y^{\prime\:\prime\:}-y=\frac{xex}{5}
y^'+ln(x)y=ln(x)	y^{\prime\:}+\ln(x)y=\ln(x)
integral of (sin(x)+cos(x))^2	\int\:(\sin(x)+\cos(x))^{2}dx
derivative of (x-3/(6x-5))	\frac{d}{dx}(\frac{x-3}{6x-5})
limit as x approaches 2 of 1/(sqrt(2-x))	\lim\:_{x\to\:2}(\frac{1}{\sqrt{2-x}})
(\partial)/(\partial y)(e^{-x}cos(y))	\frac{\partial\:}{\partial\:y}(e^{-x}\cos(y))
slope of (2,5),(3,1)	slope\:(2,5),(3,1)
integral of 0.33e^{-0.33y}	\int\:0.33e^{-0.33y}dy
integral of 4/(1+4x^2)	\int\:\frac{4}{1+4x^{2}}dx
integral from 0 to 5 of (x-20)(10x-50)	\int\:_{0}^{5}(x-20)(10x-50)dx
integral of (x^2)/(1+x)	\int\:\frac{x^{2}}{1+x}dx
derivative of f(x)=3x^4-5x^3-x^2+4x+9	derivative\:f(x)=3x^{4}-5x^{3}-x^{2}+4x+9
integral of x/(x+6)	\int\:\frac{x}{x+6}dx
integral of (4cos(x))/(sin^2(x))	\int\:\frac{4\cos(x)}{\sin^{2}(x)}dx
tangent of y=cos(x),\at x=1	tangent\:y=\cos(x),\at\:x=1
derivative of (x^3+8/(x^2-4))	\frac{d}{dx}(\frac{x^{3}+8}{x^{2}-4})
integral of 1/(sqrt(2))	\int\:\frac{1}{\sqrt{2}}dx
integral from 1 to 2 of 1/(sqrt(x-1))	\int\:_{1}^{2}\frac{1}{\sqrt{x-1}}dx
integral of (16)/(x^2-1)	\int\:\frac{16}{x^{2}-1}dx
x(dy)/(dx)-(1+x)y=xy^2	x\frac{dy}{dx}-(1+x)y=xy^{2}
integral of (3x^2+1)/(x^2sqrt(4-x^2))	\int\:\frac{3x^{2}+1}{x^{2}\sqrt{4-x^{2}}}dx
derivative of (cos(x)/(x^4))	\frac{d}{dx}(\frac{\cos(x)}{x^{4}})
derivative of (y^2/x)	\frac{d}{dx}(\frac{y^{2}}{x})
derivative of ln(1/(3x))	\frac{d}{dx}(\ln(\frac{1}{3x}))
integral of sin(3pi)t	\int\:\sin(3π)tdt
derivative of 3e^{-x^3}	\frac{d}{dx}(3e^{-x^{3}})
derivative of f(x)=x^2-3x+1	derivative\:f(x)=x^{2}-3x+1
derivative of log_{x}(e)	\frac{d}{dx}(\log_{x}(e))
integral from 1 to x of 1/(t^3+1)	\int\:_{1}^{x}\frac{1}{t^{3}+1}dt
d/(dt)((t+1)^{2/3}(2t^2-1)^3)	\frac{d}{dt}((t+1)^{\frac{2}{3}}(2t^{2}-1)^{3})
integral of ((x+6)/(x^2+11x+18))	\int\:(\frac{x+6}{x^{2}+11x+18})dx
derivative of x^6+3x^4+7x^2	\frac{d}{dx}(x^{6}+3x^{4}+7x^{2})
laplacetransform cos(pit)	laplacetransform\:\cos(πt)
f^{''}(x)=x^{(-3)/2},f^'(4)=2,f(0)=0	f^{\prime\:\prime\:}(x)=x^{\frac{-3}{2}},f^{\prime\:}(4)=2,f(0)=0
(\partial)/(\partial x)(cos(x^6-7y))	\frac{\partial\:}{\partial\:x}(\cos(x^{6}-7y))
integral from 0 to 1 of 7/(sqrt(x)(1+x))	\int\:_{0}^{1}\frac{7}{\sqrt{x}(1+x)}dx
(\partial)/(\partial y)(x)	\frac{\partial\:}{\partial\:y}(x)
limit as x approaches 0 of (x^2)cos(8/x)	\lim\:_{x\to\:0}((x^{2})\cos(\frac{8}{x}))
(\partial)/(\partial x)(-10xysin(xy^2))	\frac{\partial\:}{\partial\:x}(-10xy\sin(xy^{2}))
derivative of f(x)=(2x-x^3)(3x+7)	derivative\:f(x)=(2x-x^{3})(3x+7)
derivative of 5x^2+1	\frac{d}{dx}(5x^{2}+1)
tangent of f(x)=x^2+4/x-10,\at x=8	tangent\:f(x)=x^{2}+\frac{4}{x}-10,\at\:x=8
integral from-3 to 3 of (12-x^2)-(x^2-6)	\int\:_{-3}^{3}(12-x^{2})-(x^{2}-6)dx
integral from 1 to e of cos(ln(x))	\int\:_{1}^{e}\cos(\ln(x))dx
integral of (6x^3-3x^2+5+7x^{-1})/(x^3)	\int\:\frac{6x^{3}-3x^{2}+5+7x^{-1}}{x^{3}}dx
integral of c/x e^{-9x}	\int\:\frac{c}{x}e^{-9x}dx
integral of (sqrt(1+x))/x	\int\:\frac{\sqrt{1+x}}{x}dx
derivative of f(x)=x^{5x}	derivative\:f(x)=x^{5x}
tangent of y=x^4+9e^x,(0,9)	tangent\:y=x^{4}+9e^{x},(0,9)
2ydx+(y-2x)dy=0	2ydx+(y-2x)dy=0
y=(3x^2)(5x^4)	y=(3x^{2})(5x^{4})
(dy)/(dx)=-x^{1/3}	\frac{dy}{dx}=-x^{\frac{1}{3}}
integral of (sqrt(y^2-64))/y	\int\:\frac{\sqrt{y^{2}-64}}{y}dy
integral of ze^y+x^6	\int\:ze^{y}+x^{6}dy
derivative of sin(xsin(y))	\frac{d}{dx}(\sin(x)\sin(y))
3((dy)/(dx))+12y=4	3(\frac{dy}{dx})+12y=4
integral of (sin^3(sqrt(x)))/(sqrt(x))	\int\:\frac{\sin^{3}(\sqrt{x})}{\sqrt{x}}dx
(\partial)/(\partial x)(xln(z^4+x^6))	\frac{\partial\:}{\partial\:x}(x\ln(z^{4}+x^{6}))
derivative of f(x)=3sqrt(x-1)	derivative\:f(x)=3\sqrt{x-1}
(d^4)/(dx^4)(19e^{x^2})	\frac{d^{4}}{dx^{4}}(19e^{x^{2}})
derivative of xsqrt(a^2-x^2)	\frac{d}{dx}(x\sqrt{a^{2}-x^{2}})
integral of 1/(sqrt(-x^2-10x-24))	\int\:\frac{1}{\sqrt{-x^{2}-10x-24}}dx
limit as x approaches 3 of \|1-x-x^2\|	\lim\:_{x\to\:3}(\left\|1-x-x^{2}\right\|)
derivative of 1/(2sqrt(x)+1/(9x^{8/9)})	\frac{d}{dx}(\frac{1}{2\sqrt{x}}+\frac{1}{9x^{\frac{8}{9}}})

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