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Popular Calculus Problems

derivative of arctan(1/(3x))	\frac{d}{dx}(\arctan(\frac{1}{3x}))
sum from n=0 to infinity of 3(1/2)^n	\sum\:_{n=0}^{\infty\:}3(\frac{1}{2})^{n}
d/(d{r)}(({r})/(sqrt({r)^2+5)})	\frac{d}{d{r}}(\frac{{r}}{\sqrt{{r}^{2}+5}})
(\partial)/(\partial y)(x^2+y)	\frac{\partial\:}{\partial\:y}(x^{2}+y)
tangent of f(x)=(3x+1)/(x^2+1),(1,2)	tangent\:f(x)=\frac{3x+1}{x^{2}+1},(1,2)
limit as t approaches 3 of (2t-3)/(t-3)	\lim\:_{t\to\:3}(\frac{2t-3}{t-3})
slope of y=5sec(x)-10cos(x),(pi/3 ,5)	slope\:y=5\sec(x)-10\cos(x),(\frac{π}{3},5)
integral of (x-3)sqrt(x+3)	\int\:(x-3)\sqrt{x+3}dx
f(x)=4-x	f(x)=4-x
sum from n=0 to infinity}2^{n+1 of-2^n	\sum\:_{n=0}^{\infty\:}2^{n+1}-2^{n}
(dy)/(dx)+2y=1,y(0)= 5/2	\frac{dy}{dx}+2y=1,y(0)=\frac{5}{2}
integral of (x-1)/(x^3-2x^2)	\int\:\frac{x-1}{x^{3}-2x^{2}}dx
derivative of y=arcsin(3sqrt(5x))	derivative\:y=\arcsin(3\sqrt{5x})
limit as x approaches 1 of 2sqrt(3x^2+1)	\lim\:_{x\to\:1}(2\sqrt{3x^{2}+1})
area y= 1/(8x^2),y=x,y= x/6	area\:y=\frac{1}{8x^{2}},y=x,y=\frac{x}{6}
(\partial)/(\partial z)(2xyz^{-1})	\frac{\partial\:}{\partial\:z}(2xyz^{-1})
area x^2+1,2	area\:x^{2}+1,2
integral of (3x^2)/(sqrt(1-x^3))	\int\:\frac{3x^{2}}{\sqrt{1-x^{3}}}dx
derivative of (x^2+x+1/(x^3-3))	\frac{d}{dx}(\frac{x^{2}+x+1}{x^{3}-3})
y^2dx+(2xy+1)dy=0,y(9)=90	y^{2}dx+(2xy+1)dy=0,y(9)=90
limit as x approaches 0+of tan^x(2x)	\lim\:_{x\to\:0+}(\tan^{x}(2x))
derivative of-ax-d/(x^2)	\frac{d}{dx}(-ax-\frac{d}{x^{2}})
integral of e^{-x}*ln(x)	\int\:e^{-x}\cdot\:\ln(x)dx
(\partial)/(\partial x)(x^2y-y^2)	\frac{\partial\:}{\partial\:x}(x^{2}y-y^{2})
integral of (sec(x))/(sec(x)+tan(x))	\int\:\frac{\sec(x)}{\sec(x)+\tan(x)}dx
limit as x approaches 2+of 3/(x-2)	\lim\:_{x\to\:2+}(\frac{3}{x-2})
(\partial)/(\partial z)(3ze^{xyz})	\frac{\partial\:}{\partial\:z}(3ze^{xyz})
(d^3)/(dx^3)(sin(3x))	\frac{d^{3}}{dx^{3}}(\sin(3x))
integral of-4xln(x)	\int\:-4x\ln(x)dx
derivative of (ln(x))^2	derivative\:(\ln(x))^{2}
derivative of (-xsin(x-cos(x))/(x^2))	\frac{d}{dx}(\frac{-x\sin(x)-\cos(x)}{x^{2}})
integral from 1 to 2 of x*ln(x)	\int\:_{1}^{2}x\cdot\:\ln(x)dx
sum from n=0 to infinity of 1/((n^2+1))	\sum\:_{n=0}^{\infty\:}\frac{1}{(n^{2}+1)}
tangent of y= 2/(x-6),(8,1)	tangent\:y=\frac{2}{x-6},(8,1)
5x-6ysqrt((x^2+1))(dy)/(dx)=0	5x-6y\sqrt{(x^{2}+1)}\frac{dy}{dx}=0
2yy^'+2=y^2+2x,y(0)=7	2yy^{\prime\:}+2=y^{2}+2x,y(0)=7
integral of 16arctan(sqrt(x))	\int\:16\arctan(\sqrt{x})dx
derivative of x^2,x+2xcos(x-2sec(x))	\frac{d}{dx}(x^{2},x+2x\cos(x)-2\sec(x))
derivative of ln(2cos(x))	\frac{d}{dx}(\ln(2\cos(x)))
area x^3-x^2-x,x	area\:x^{3}-x^{2}-x,x
area y=-x,y=-8x+13,[0, 13/8 ]	area\:y=-x,y=-8x+13,[0,\frac{13}{8}]
(2x+1)(dy)/(dx)=4	(2x+1)\frac{dy}{dx}=4
integral of 1/(4+5x^6)(30x^5)	\int\:\frac{1}{4+5x^{6}}(30x^{5})dx
derivative of x(2x+7)^{1/3}	derivative\:x(2x+7)^{\frac{1}{3}}
t^2y^{''}+6ty^'-6y=0	t^{2}y^{\prime\:\prime\:}+6ty^{\prime\:}-6y=0
(\partial)/(\partial x)((x^3-y^2)^{(-1)})	\frac{\partial\:}{\partial\:x}((x^{3}-y^{2})^{(-1)})
derivative of 4x^2+3x+2	\frac{d}{dx}(4x^{2}+3x+2)
derivative of y=e^e	derivative\:y=e^{e}
area f(x)=x(x^2-8x+18),g(x)=x^2	area\:f(x)=x(x^{2}-8x+18),g(x)=x^{2}
integral of x^2(1-x)	\int\:x^{2}(1-x)dx
inverse oflaplace 1/((s+2)^3)	inverselaplace\:\frac{1}{(s+2)^{3}}
(\partial)/(\partial x)(x^2ysin(xy))	\frac{\partial\:}{\partial\:x}(x^{2}y\sin(xy))
integral of (sin(x))/(sqrt(x))	\int\:\frac{\sin(x)}{\sqrt{x}}dx
(\partial)/(\partial x)(ax^2+bx+c)	\frac{\partial\:}{\partial\:x}(ax^{2}+bx+c)
integral from 0 to 1 of 1/((2x-3)^2)	\int\:_{0}^{1}\frac{1}{(2x-3)^{2}}dx
derivative of (192/(x^4))	\frac{d}{dx}(\frac{192}{x^{4}})
derivative of sin^2(cos(4x))	\frac{d}{dx}(\sin^{2}(\cos(4x)))
(dy)/(dx)=sqrt(13x+y)-13	\frac{dy}{dx}=\sqrt{13x+y}-13
integral from 0 to pi of x^2cos(x)	\int\:_{0}^{π}x^{2}\cos(x)dx
integral of (4x^2+13x-9)/(x^3+2x^2-3x)	\int\:\frac{4x^{2}+13x-9}{x^{3}+2x^{2}-3x}dx
(dy)/(dt)+3y=cos(2t),y(0)=-1	\frac{dy}{dt}+3y=\cos(2t),y(0)=-1
integral of (a+bsin^3(t))/(cos^2(t))	\int\:\frac{a+b\sin^{3}(t)}{\cos^{2}(t)}dt
integral of-32x	\int\:-32xdx
integral from 0 to 2 of 1/(x^2-6x+5)	\int\:_{0}^{2}\frac{1}{x^{2}-6x+5}dx
derivative of arctan(x-pi/4)	\frac{d}{dx}(\arctan(x)-\frac{π}{4})
tangent of f(x)=3sin(x)	tangent\:f(x)=3\sin(x)
laplacetransform e^{6-2t}	laplacetransform\:e^{6-2t}
integral from 0 to 1 of x^3(2x^4+3)^2	\int\:_{0}^{1}x^{3}(2x^{4}+3)^{2}dx
inverse oflaplace (10)/(2s+1)	inverselaplace\:\frac{10}{2s+1}
integral of ((x+5))/((x^2+16))	\int\:\frac{(x+5)}{(x^{2}+16)}dx
integral of 1/(sqrt(x^3))	\int\:\frac{1}{\sqrt{x^{3}}}dx
x^2y^{''}-3xy^'+3y=0	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}+3y=0
integral from 0 to 2 of-8x^3sqrt(x^2+4)	\int\:_{0}^{2}-8x^{3}\sqrt{x^{2}+4}dx
integral from 2 to 12 of 1/(27t+36)	\int\:_{2}^{12}\frac{1}{27t+36}dt
integral of (x+2)/((x^2+x+1))	\int\:\frac{x+2}{(x^{2}+x+1)}dx
slope of x^2-3x-4	slope\:x^{2}-3x-4
derivative of y=7x^3	derivative\:y=7x^{3}
(\partial)/(\partial x)(ln(x^2+y^2+4))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{2}+4))
integral of (x^2)/(1-x^6)	\int\:\frac{x^{2}}{1-x^{6}}dx
integral of (2x-5)/((x+2)(x+3))	\int\:\frac{2x-5}{(x+2)(x+3)}dx
integral of sqrt(x)cos(sqrt(x))	\int\:\sqrt{x}\cos(\sqrt{x})dx
slope of (3x^{1/2})/2	slope\:\frac{3x^{\frac{1}{2}}}{2}
limit as x approaches-7 of (6x+42)/(x+7)	\lim\:_{x\to\:-7}(\frac{6x+42}{x+7})
derivative of {u}(x(x)^n)	\frac{d}{dx}({u}(x)(x)^{n})
tangent of f(x)=3x^3+4x^2,(-1,1)	tangent\:f(x)=3x^{3}+4x^{2},(-1,1)
limit as x approaches 3+of 2x^2-5	\lim\:_{x\to\:3+}(2x^{2}-5)
derivative of 7^{2x}	\frac{d}{dx}(7^{2x})
integral of 1/(1+y)	\int\:\frac{1}{1+y}dy
integral of xsqrt(9+x^2)	\int\:x\sqrt{9+x^{2}}dx
derivative of y= 1/4 x^2-1/2 ln(x)	derivative\:y=\frac{1}{4}x^{2}-\frac{1}{2}\ln(x)
sum from n=1 to infinity of 1/(e^{n^2)}	\sum\:_{n=1}^{\infty\:}\frac{1}{e^{n^{2}}}
(\partial)/(\partial y)(2xe^y)	\frac{\partial\:}{\partial\:y}(2xe^{y})
tangent of 15-x^2	tangent\:15-x^{2}
d/(dt)((1-3t^2)/(1-2t))	\frac{d}{dt}(\frac{1-3t^{2}}{1-2t})
derivative of 1/((x+1^2))	\frac{d}{dx}(\frac{1}{(x+1)^{2}})
limit as x approaches 0 of ((5x)^{-1}-5^{-1})/x	\lim\:_{x\to\:0}(\frac{(5x)^{-1}-5^{-1}}{x})
derivative of f(x)=(2x+5)/(3x-2)	derivative\:f(x)=\frac{2x+5}{3x-2}
(\partial)/(\partial y)(y^2e^{2x})	\frac{\partial\:}{\partial\:y}(y^{2}e^{2x})
derivative of (-pix^2-4x^2+64x/8)	\frac{d}{dx}(\frac{-πx^{2}-4x^{2}+64x}{8})
(x-1)y^{''}-xy^'+y=0	(x-1)y^{\prime\:\prime\:}-xy^{\prime\:}+y=0

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