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Popular Calculus Problems

derivative of 1-sqrt(cos(x))	\frac{d}{dx}(1-\sqrt{\cos(x)})
y'=0.0013y(3000-y)	y\prime\:=0.0013y(3000-y)
tangent of y=3x^3-x^2+7,(2,27)	tangent\:y=3x^{3}-x^{2}+7,(2,27)
integral of (x+4)(x+2)	\int\:(x+4)(x+2)dx
integral of (4x^2)	\int\:(4x^{2})dx
area y=13x,y=x^2	area\:y=13x,y=x^{2}
integral of ((2+sqrt(x)+x))/x	\int\:\frac{(2+\sqrt{x}+x)}{x}dx
integral of 1/(7(x^2+1))	\int\:\frac{1}{7(x^{2}+1)}dx
derivative of (x^3+7^6)	\frac{d}{dx}((x^{3}+7)^{6})
(\partial)/(\partial x)(x^2+y^2-2xy)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}-2xy)
limit as t approaches 1 of (ln(t))/(t-1)	\lim\:_{t\to\:1}(\frac{\ln(t)}{t-1})
y^'+xy=4xy^{7/2}	y^{\prime\:}+xy=4xy^{\frac{7}{2}}
integral from 0 to pi/2 of 4cos^2(x)	\int\:_{0}^{\frac{π}{2}}4\cos^{2}(x)dx
derivative of (-9x^2+25^2)	\frac{d}{dx}((-9x^{2}+25)^{2})
integral of 1/(x(ln(x))^7)	\int\:\frac{1}{x(\ln(x))^{7}}dx
derivative of-(6x/((x^2+9)^2))	\frac{d}{dx}(-\frac{6x}{(x^{2}+9)^{2}})
derivative of 0.7x^35^x	derivative\:0.7x^{3}5^{x}
integral of sinh(x	\int\:\sinh(d)xdx
tangent of f(x)=sqrt(5x+6),\at x=6	tangent\:f(x)=\sqrt{5x+6},\at\:x=6
5*(dQ)/(dt)+Q/3 =0	5\cdot\:\frac{dQ}{dt}+\frac{Q}{3}=0
f(x)=5e^x	f(x)=5e^{x}
x^2(dy)/(dx)+xy=x^3	x^{2}\frac{dy}{dx}+xy=x^{3}
tangent of-x^2+4sqrt(x),\at x=4	tangent\:-x^{2}+4\sqrt{x},\at\:x=4
integral of x+y+1	\int\:x+y+1dx
y^'=7x+y,y(0)=5	y^{\prime\:}=7x+y,y(0)=5
integral of 1/(sqrt(x^2-2x))	\int\:\frac{1}{\sqrt{x^{2}-2x}}dx
area 3x^2,(1,3)	area\:3x^{2},(1,3)
integral from 0 to pi of 12sin^4(x)	\int\:_{0}^{π}12\sin^{4}(x)dx
integral from 1 to 2 of (7x+x^2)	\int\:_{1}^{2}(7x+x^{2})dx
derivative of cos(2^x)	derivative\:\cos(2^{x})
(-19xy^2+10y)+(-19x^2y+10x)y^'=0	(-19xy^{2}+10y)+(-19x^{2}y+10x)y^{\prime\:}=0
x^2y(dy)/(dx)=e^y	x^{2}y\frac{dy}{dx}=e^{y}
limit as x approaches 2-of (x-2)/(\|x-2\|)	\lim\:_{x\to\:2-}(\frac{x-2}{\left\|x-2\right\|})
y^'=((3x^2-e^x))/(2y-5)	y^{\prime\:}=\frac{(3x^{2}-e^{x})}{2y-5}
y^{''}+11y^'+30y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+11y^{\prime\:}+30y=0,y(0)=1,y^{\prime\:}(0)=0
integral from 1 to 4 of 3xe^x	\int\:_{1}^{4}3xe^{x}dx
integral from 1 to 5 of (ln(R))/(R^2)	\int\:_{1}^{5}\frac{\ln(R)}{R^{2}}dR
(\partial)/(\partial x)(-1/(x^2))	\frac{\partial\:}{\partial\:x}(-\frac{1}{x^{2}})
(dy)/(dx)=(x+y-5)^2	\frac{dy}{dx}=(x+y-5)^{2}
integral of sqrt(1+y^2)	\int\:\sqrt{1+y^{2}}dy
derivative of 2xy+x^2-1	\frac{d}{dx}(2xy+x^{2}-1)
tangent of ((x^4+1))/(e^x+2x+1)	tangent\:\frac{(x^{4}+1)}{e^{x}+2x+1}
derivative of 12x^3-24x^2	derivative\:12x^{3}-24x^{2}
f(I)=I^{22}	f(I)=I^{22}
integral of (x^2+8)/(x^4-x^3-2x^2)	\int\:\frac{x^{2}+8}{x^{4}-x^{3}-2x^{2}}dx
limit as x approaches+x of (x^2-1)/(x-1)	\lim\:_{x\to\:+x}(\frac{x^{2}-1}{x-1})
derivative of f(x)= 7/((x^2-10)^4)	derivative\:f(x)=\frac{7}{(x^{2}-10)^{4}}
derivative of f(x)= 4/x-16sec(x)	derivative\:f(x)=\frac{4}{x}-16\sec(x)
derivative of 6e^{-x/2}	\frac{d}{dx}(6e^{-\frac{x}{2}})
integral of-3x^4-6x^2+8	\int\:-3x^{4}-6x^{2}+8dx
limit as x approaches 0 of xcsc(pix)	\lim\:_{x\to\:0}(x\csc(πx))
limit as x approaches 1/3 of x^4	\lim\:_{x\to\:\frac{1}{3}}(x^{4})
limit as x approaches+0+of x^{sqrt(x)}	\lim\:_{x\to\:+0+}(x^{\sqrt{x}})
limit as (x,y) approaches (0,0) of 1	\lim\:_{(x,y)\to\:(0,0)}(1)
limit as x approaches 3-of-x^2+6x-5	\lim\:_{x\to\:3-}(-x^{2}+6x-5)
area y=x^2-3x,y=3x+7	area\:y=x^{2}-3x,y=3x+7
taylor cot(x)	taylor\:\cot(x)
integral of-2e^{3x}	\int\:-2e^{3x}dx
integral of 3/2 ln\|x^3\|+1	\int\:\frac{3}{2}\ln\left\|x^{3}\right\|+1dx
derivative of f(x)= x/(x-1)	derivative\:f(x)=\frac{x}{x-1}
tangent of f(x)=3-5x+2x^2,(-9,210)	tangent\:f(x)=3-5x+2x^{2},(-9,210)
(x+y)^2dx+(2xy+x^2-9)dy=0	(x+y)^{2}dx+(2xy+x^{2}-9)dy=0
limit as x approaches infinity of x/(2x)	\lim\:_{x\to\:\infty\:}(\frac{x}{2x})
(\partial)/(\partial x)(x/(2+y))	\frac{\partial\:}{\partial\:x}(\frac{x}{2+y})
f(t)=cos(ln(t))	f(t)=\cos(\ln(t))
xy^'-y= 5/2 xln(x)	xy^{\prime\:}-y=\frac{5}{2}x\ln(x)
implicit (dy)/(dx),3e^{xy}-x=0	implicit\:\frac{dy}{dx},3e^{xy}-x=0
integral of z^2	\int\:z^{2}dz
(\partial)/(\partial t)((x-ct)^4+(x+ct)^4)	\frac{\partial\:}{\partial\:t}((x-ct)^{4}+(x+ct)^{4})
integral of ((4x+2))/(x^3-x^2+2x)	\int\:\frac{(4x+2)}{x^{3}-x^{2}+2x}dx
y^'=2ty^2	y^{\prime\:}=2ty^{2}
inverse oflaplace (e^{-s})/((s+1)^2)	inverselaplace\:\frac{e^{-s}}{(s+1)^{2}}
integral of-e^{-x}x	\int\:-e^{-x}xdx
integral from 0 to 10 of f(x)	\int\:_{0}^{10}f(x)dx
integral of (x^4)/(sqrt(x^5+3))	\int\:\frac{x^{4}}{\sqrt{x^{5}+3}}dx
integral of sqrt(p)+4	\int\:\sqrt{p}+4dp
integral of x^3(2-x^2)^{12}	\int\:x^{3}(2-x^{2})^{12}dx
integral of 10x^9	\int\:10x^{9}dx
derivative of cos(ln(6x))	\frac{d}{dx}(\cos(\ln(6x)))
integral of 1/((z^2-6z+18)^{3/2)}	\int\:\frac{1}{(z^{2}-6z+18)^{\frac{3}{2}}}dz
limit as x approaches 0 of-1	\lim\:_{x\to\:0}(-1)
tangent of e^{x^7}	tangent\:e^{x^{7}}
x^2y^{''}+xy^'+4=0	x^{2}y^{\prime\:\prime\:}+xy^{\prime\:}+4=0
y^{''}+7y^'-3y=0,y(0)=-3,y^'(0)=7	y^{\prime\:\prime\:}+7y^{\prime\:}-3y=0,y(0)=-3,y^{\prime\:}(0)=7
integral of (2x^{3/2})/3	\int\:\frac{2x^{\frac{3}{2}}}{3}dx
(dy)/(dx)=(x^2y^2)/(1+y)	\frac{dy}{dx}=\frac{x^{2}y^{2}}{1+y}
limit as x approaches 2-of 4x-5	\lim\:_{x\to\:2-}(4x-5)
derivative of y=2e^x-e^{x+1}+e^{2/3}-5pi^2	derivative\:y=2e^{x}-e^{x+1}+e^{\frac{2}{3}}-5π^{2}
y^'+10y=6	y^{\prime\:}+10y=6
laplacetransform 4t^2-5sin(3t)	laplacetransform\:4t^{2}-5\sin(3t)
integral from 0 to 5 of (3x-4)/(x+1)	\int\:_{0}^{5}\frac{3x-4}{x+1}dx
limit as x approaches 0-of 1/(x^2)-1/x	\lim\:_{x\to\:0-}(\frac{1}{x^{2}}-\frac{1}{x})
integral from 1 to 3 of e^{x^2}	\int\:_{1}^{3}e^{x^{2}}dx
integral from 1 to b of 1/((x+1)^2)	\int\:_{1}^{b}\frac{1}{(x+1)^{2}}dx
integral of 2e^{-4x}	\int\:2e^{-4x}dx
integral of sqrt((1-x)/x)	\int\:\sqrt{\frac{1-x}{x}}dx
tangent of y=e^{6x}cos(pix),(0,1)	tangent\:y=e^{6x}\cos(πx),(0,1)
(\partial)/(\partial x)(-3xy)	\frac{\partial\:}{\partial\:x}(-3xy)
integral of cos^4(5-x)sin(5-x)	\int\:\cos^{4}(5-x)\sin(5-x)dx
(dy)/(dx)=(3+y)/(1-2x),y(0)=0	\frac{dy}{dx}=\frac{3+y}{1-2x},y(0)=0

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