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Popular Calculus Problems

(\partial)/(\partial x)(x^3+y)	\frac{\partial\:}{\partial\:x}(x^{3}+y)
tangent of f(x)=2x^2+1,(1,3)	tangent\:f(x)=2x^{2}+1,(1,3)
derivative of xln(x^2+5)	\frac{d}{dx}(x\ln(x^{2}+5))
integral from 1 to 10 of 1/(x^3)	\int\:_{1}^{10}\frac{1}{x^{3}}dx
(\partial)/(\partial x)(4cos(xy^2))	\frac{\partial\:}{\partial\:x}(4\cos(xy^{2}))
integral of (x^3-1/(2x)+1)	\int\:(x^{3}-\frac{1}{2x}+1)dx
limit as w approaches-1+of w+\|3w+3\|	\lim\:_{w\to\:-1+}(w+\left\|3w+3\right\|)
integral of-sin(-x)	\int\:-\sin(-x)dx
2x^2y^{''}+6xy^'+2y=0	2x^{2}y^{\prime\:\prime\:}+6xy^{\prime\:}+2y=0
(\partial)/(\partial x)(sqrt(x^3+x))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{3}+x})
integral from b to 1 of 3ln(x)	\int\:_{b}^{1}3\ln(x)dx
integral of 5x 3/2	\int\:5x\frac{3}{2}dx
(dy)/(dx)-(sin(x))y=2sin(x)	\frac{dy}{dx}-(\sin(x))y=2\sin(x)
derivative of (e^{-x}/x)	\frac{d}{dx}(\frac{e^{-x}}{x})
integral from-1 to 1 of e^y-(y^2-9)	\int\:_{-1}^{1}e^{y}-(y^{2}-9)dy
(14-6y+e-3x)dx-2dy=0	(14-6y+e-3x)dx-2dy=0
integral from 0 to 6 of pi/8 (6-x)^2	\int\:_{0}^{6}\frac{π}{8}(6-x)^{2}dx
integral of sin^4(xco)s^2x	\int\:\sin^{4}(xco)s^{2}xdx
derivative of y=(cos(x))/(x^7)	derivative\:y=\frac{\cos(x)}{x^{7}}
limit as x approaches 0 of (sin(2x))/x	\lim\:_{x\to\:0}(\frac{\sin(2x)}{x})
y^'=-y^3,y(0)=2	y^{\prime\:}=-y^{3},y(0)=2
(\partial)/(\partial x)(7xcos(xy))	\frac{\partial\:}{\partial\:x}(7x\cos(xy))
(dx)/(dt)=1-t+x-tx	\frac{dx}{dt}=1-t+x-tx
7y^{''}+y=0	7y^{\prime\:\prime\:}+y=0
integral of e^{4x} 1/5	\int\:e^{4x}\frac{1}{5}dx
(dy)/(dt)=(5+sin(t))*(y/5)	\frac{dy}{dt}=(5+\sin(t))\cdot\:(\frac{y}{5})
integral of (x+11)/((x-4)(x+1))	\int\:\frac{x+11}{(x-4)(x+1)}dx
derivative of y=sqrt(ax+b)	derivative\:y=\sqrt{ax+b}
area x^2=y,x^2=-(y-2)	area\:x^{2}=y,x^{2}=-(y-2)
(\partial)/(\partial x)(x+3y^{1/3})	\frac{\partial\:}{\partial\:x}(x+3y^{\frac{1}{3}})
-y^'+(3y)/x =(y^2)/x	-y^{\prime\:}+\frac{3y}{x}=\frac{y^{2}}{x}
derivative of (7x^2+3x+7/(sqrt(x)))	\frac{d}{dx}(\frac{7x^{2}+3x+7}{\sqrt{x}})
limit as x approaches 0+of 7(1/x-cot(x))	\lim\:_{x\to\:0+}(7(\frac{1}{x}-\cot(x)))
y^{''}+9y=sec^2(3x)	y^{\prime\:\prime\:}+9y=\sec^{2}(3x)
derivative of y=x^{sqrt(x)}	derivative\:y=x^{\sqrt{x}}
limit as x approaches+pi+of csc(x)	\lim\:_{x\to\:+π+}(\csc(x))
derivative of (x-42^2-3xln((x-100)^2))	\frac{d}{dx}((x-42)^{2}-3x\ln((x-100)^{2}))
(e^xy)dy=(e^{-y}+e^{-2x-y})dx	(e^{x}y)dy=(e^{-y}+e^{-2x-y})dx
derivative of ln(t)	derivative\:\ln(t)
limit as x approaches 5 of 2x^2-3x+4	\lim\:_{x\to\:5}(2x^{2}-3x+4)
derivative of-(7x)/y	derivative\:-\frac{7x}{y}
maclaurin 1/2 (e^x+e^{-x})	maclaurin\:\frac{1}{2}(e^{x}+e^{-x})
integral of (k/(2018))x^2	\int\:(\frac{k}{2018})x^{2}dx
integral of (x^2)/(2(x^2+1))	\int\:\frac{x^{2}}{2(x^{2}+1)}dx
integral of 1/(e^{2x)-1}	\int\:\frac{1}{e^{2x}-1}dx
integral of 1/(sqrt(8x+2x^2))	\int\:\frac{1}{\sqrt{8x+2x^{2}}}dx
limit as x approaches 2 of 2x^2+a/2 x-4	\lim\:_{x\to\:2}(2x^{2}+\frac{a}{2}x-4)
derivative of (x^2-x+2)^3	derivative\:(x^{2}-x+2)^{3}
integral of (sqrt(1+e^{-x)})/(e^x)	\int\:\frac{\sqrt{1+e^{-x}}}{e^{x}}dx
laplacetransform f(t)=t^2e^{,\at}	laplacetransform\:f(t)=t^{2}e^{,\at\:}
y^'+yx^3=4x^3	y^{\prime\:}+yx^{3}=4x^{3}
limit as x approaches 0 of sqrt(x^2+9)-3	\lim\:_{x\to\:0}(\sqrt{x^{2}+9}-3)
sum from n=0 to infinity of 4(2/5)^n	\sum\:_{n=0}^{\infty\:}4(\frac{2}{5})^{n}
tangent of f(x)=xsqrt(x),\at x=3	tangent\:f(x)=x\sqrt{x},\at\:x=3
(\partial)/(\partial x)(-1/4 (y^2+x^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{4}(y^{2}+x^{2}))
(\partial)/(\partial x)(e^{-3t}sin(x+5t))	\frac{\partial\:}{\partial\:x}(e^{-3t}\sin(x+5t))
integral of (x^2)/(x^2+7)	\int\:\frac{x^{2}}{x^{2}+7}dx
limit as x approaches 2 of (x^3)/2	\lim\:_{x\to\:2}(\frac{x^{3}}{2})
integral from 1 to 3 of 1	\int\:_{1}^{3}1
y^{''}-y=t^2	y^{\prime\:\prime\:}-y=t^{2}
taylor z/((1-z^2))	taylor\:\frac{z}{(1-z^{2})}
integral of (x^4-5x^2+7)/(x^4)	\int\:\frac{x^{4}-5x^{2}+7}{x^{4}}dx
integral of (t-x)^2	\int\:(t-x)^{2}dx
integral of-5x^2sec^2(3x^3)tan^5(3x^3)	\int\:-5x^{2}\sec^{2}(3x^{3})\tan^{5}(3x^{3})dx
area x^3-x,x^2+x,-1,2	area\:x^{3}-x,x^{2}+x,-1,2
derivative of (6x)/(sqrt(x^2+4))	derivative\:\frac{6x}{\sqrt{x^{2}+4}}
(dy)/(dx)=x^2y^2	\frac{dy}{dx}=x^{2}y^{2}
tangent of f(x)=(ln(x))^5,\at x=4	tangent\:f(x)=(\ln(x))^{5},\at\:x=4
limit as x approaches 0 of 1+cos(x)	\lim\:_{x\to\:0}(1+\cos(x))
integral of 3xe^{-x^2}	\int\:3xe^{-x^{2}}dx
integral of sin(x)ln(cos(x))	\int\:\sin(x)\ln(\cos(x))dx
limit as x approaches 2 of (4-x^2)/(x-2)	\lim\:_{x\to\:2}(\frac{4-x^{2}}{x-2})
e^{-2u+v^2}((1+u)du+2uvdv)=0	e^{-2u+v^{2}}((1+u)du+2uvdv)=0
derivative of 5cos(x-16/25)	derivative\:5\cos(x-\frac{16}{25})
integral of x^3cos(x/2)	\int\:x^{3}\cos(\frac{x}{2})dx
-9x^2y+y^'=9x^2	-9x^{2}y+y^{\prime\:}=9x^{2}
integral of cos(t^5)	\int\:\cos(t^{5})dt
derivative of 3/5 x^{5/3}-3/4 x^{1/3}	derivative\:\frac{3}{5}x^{\frac{5}{3}}-\frac{3}{4}x^{\frac{1}{3}}
(\partial)/(\partial y)(4y^3cos(2x))	\frac{\partial\:}{\partial\:y}(4y^{3}\cos(2x))
integral of 1/(xsqrt(1+x))	\int\:\frac{1}{x\sqrt{1+x}}dx
integral of (-1)/(2(x+1))	\int\:\frac{-1}{2(x+1)}dx
integral of x^4ln(3x)	\int\:x^{4}\ln(3x)dx
derivative of (x^2+1)^3(x^2+2)^6	derivative\:(x^{2}+1)^{3}(x^{2}+2)^{6}
integral from-ln(4) to 0 of 3sqrt(3)e^t	\int\:_{-\ln(4)}^{0}3\sqrt{3}e^{t}dt
derivative of 1/(6x^2+5)	derivative\:\frac{1}{6x^{2}+5}
integral of 15x^{29}cos(x^{15})	\int\:15x^{29}\cos(x^{15})dx
(d^2)/(dx^2)(cos(3x))	\frac{d^{2}}{dx^{2}}(\cos(3x))
derivative of ln(1-ln(x))	\frac{d}{dx}(\ln(1-\ln(x)))
derivative of sqrt(1+e^{2x)}	derivative\:\sqrt{1+e^{2x}}
slope of f(θ)=4sin(θ)-θ	slope\:f(θ)=4\sin(θ)-θ
(\partial)/(\partial x)(x^4+y^4-2xy)	\frac{\partial\:}{\partial\:x}(x^{4}+y^{4}-2xy)
integral of (x^2+3x+5)/(x+1)	\int\:\frac{x^{2}+3x+5}{x+1}dx
integral from-2 to 2 of (e^x-e^{-x})^2	\int\:_{-2}^{2}(e^{x}-e^{-x})^{2}dx
integral from 1/2 to e/2 of 256x^3ln(2x)	\int\:_{\frac{1}{2}}^{\frac{e}{2}}256x^{3}\ln(2x)dx
derivative of e^{-0.5t}	derivative\:e^{-0.5t}
sum from n=1 to infinity of n^5e^{-n}	\sum\:_{n=1}^{\infty\:}n^{5}e^{-n}
derivative of x^{-3x}	\frac{d}{dx}(x^{-3x})
derivative of csch(x)	\frac{d}{dx}(\csch(x))
(3\sqrt[3]{x})^'	(3\sqrt[3]{x})^{\prime\:}
derivative of f(x)=e^xcos(x)	derivative\:f(x)=e^{x}\cos(x)

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