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Popular Calculus Problems

x(dy)/(dx)-2y=x^2	x\frac{dy}{dx}-2y=x^{2}
d/(dy)(-e^{-xy})	\frac{d}{dy}(-e^{-xy})
integral of (sqrt(25-x^2))/x	\int\:\frac{\sqrt{25-x^{2}}}{x}dx
integral of (sec(x)tan(x))/(2sec(x)+3)	\int\:\frac{\sec(x)\tan(x)}{2\sec(x)+3}dx
integral of (x+2)(2x-1)	\int\:(x+2)(2x-1)dx
derivative of 3x^2+6	\frac{d}{dx}(3x^{2}+6)
derivative of 1-(a/x ^{b-1})	\frac{d}{dx}(1-(\frac{a}{x})^{b-1})
limit as x approaches 0 of 4e^x	\lim\:_{x\to\:0}(4e^{x})
derivative of x^{11}arccot(x)	derivative\:x^{11}\arccot(x)
limit as t approaches (0) of ln(t)	\lim\:_{t\to\:(0)}(\ln(t))
y^'=(2-3y)/(200+x)	y^{\prime\:}=\frac{2-3y}{200+x}
y^{''}+2y^'=sin(t)	y^{\prime\:\prime\:}+2y^{\prime\:}=\sin(t)
derivative of f(x)=-1/2 (x^{-2}-x^4)	derivative\:f(x)=-\frac{1}{2}(x^{-2}-x^{4})
integral of sin(2x)*cos(2x)	\int\:\sin(2x)\cdot\:\cos(2x)dx
sum from n=1 to infinity of 1/n x^n	\sum\:_{n=1}^{\infty\:}\frac{1}{n}x^{n}
sum from n=1 to infinity of (6/4)^n	\sum\:_{n=1}^{\infty\:}(\frac{6}{4})^{n}
integral of (1-x)	\int\:(1-x)dx
(\partial)/(\partial x)(sin(4x-7y))	\frac{\partial\:}{\partial\:x}(\sin(4x-7y))
((x+1)dy)/(dx)=-y+10	\frac{(x+1)dy}{dx}=-y+10
derivative of sqrt(x^2+45)	\frac{d}{dx}(\sqrt{x^{2}+45})
limit as x approaches infinity of 8,x	\lim\:_{x\to\:\infty\:}(8,x)
integral from 0 to pi/2 of (sin(x))^5	\int\:_{0}^{\frac{π}{2}}(\sin(x))^{5}dx
(dy)/(dx)-y= 11/8 e^{-x/3}	\frac{dy}{dx}-y=\frac{11}{8}e^{-\frac{x}{3}}
limit as x approaches-4 of 6/(x+5)	\lim\:_{x\to\:-4}(\frac{6}{x+5})
integral of sqrt(-x^2+16)	\int\:\sqrt{-x^{2}+16}dx
(\partial)/(\partial x)(ln(4x+7y+3z))	\frac{\partial\:}{\partial\:x}(\ln(4x+7y+3z))
derivative of 2cos(x+2sin(x))	\frac{d}{dx}(2\cos(x)+2\sin(x))
(\partial)/(\partial x)(x^3y-xy^3+sqrt(xy))	\frac{\partial\:}{\partial\:x}(x^{3}y-xy^{3}+\sqrt{xy})
(\partial)/(\partial y)(2x^2-x^2y^3+y^2)	\frac{\partial\:}{\partial\:y}(2x^{2}-x^{2}y^{3}+y^{2})
derivative of 9^2	\frac{d}{dx}(9^{2})
integral of x\sqrt[3]{6x+1}	\int\:x\sqrt[3]{6x+1}dx
tangent of y=(1+2x)^2,(2,25)	tangent\:y=(1+2x)^{2},(2,25)
y^{''}+y^'-2y=1-2x^2	y^{\prime\:\prime\:}+y^{\prime\:}-2y=1-2x^{2}
limit as t approaches 1 of sin(pit)	\lim\:_{t\to\:1}(\sin(πt))
d/(dj)(3i+2j)	\frac{d}{dj}(3i+2j)
derivative of \sqrt[3]{cos(x^3})	\frac{d}{dx}(\sqrt[3]{\cos(x^{3})})
integral from 0 to 1 of x(1-x)sin(npix)	\int\:_{0}^{1}x(1-x)\sin(nπx)dx
derivative of x^{-7}	derivative\:x^{-7}
integral from 1 to infinity of 3xe^{-x}	\int\:_{1}^{\infty\:}3xe^{-x}dx
integral of tanh^2(3x)	\int\:\tanh^{2}(3x)dx
sum from n=0 to infinity of n*a^n	\sum\:_{n=0}^{\infty\:}n\cdot\:a^{n}
d/(dz)(e^{xz})	\frac{d}{dz}(e^{xz})
derivative of e^{-x+1}x-2e^{-x+1}	derivative\:e^{-x+1}x-2e^{-x+1}
tangent of f(x)= 5/x ,(-4,-5/4)	tangent\:f(x)=\frac{5}{x},(-4,-\frac{5}{4})
derivative of-(x^8)/(y^8)	derivative\:-\frac{x^{8}}{y^{8}}
area x^2-4x,x+6	area\:x^{2}-4x,x+6
integral of (31)/(31+e^x)	\int\:\frac{31}{31+e^{x}}dx
integral of (3x+1)(3x^2+2x)^{3/4}	\int\:(3x+1)(3x^{2}+2x)^{\frac{3}{4}}dx
tangent of y=4x^4+3x-5,(1,2)	tangent\:y=4x^{4}+3x-5,(1,2)
tangent of f(x)= 1/(2+3x),\at x=1	tangent\:f(x)=\frac{1}{2+3x},\at\:x=1
derivative of y=sqrt(-3x-5)	derivative\:y=\sqrt{-3x-5}
(\partial)/(\partial x)(-2(y+1)x^{-3})	\frac{\partial\:}{\partial\:x}(-2(y+1)x^{-3})
derivative of sin^2(x)-cos^2(x)	derivative\:\sin^{2}(x)-\cos^{2}(x)
2sin(x)y^'+ycos(x)=y^2cos(x)	2\sin(x)y^{\prime\:}+y\cos(x)=y^{2}\cos(x)
(\partial)/(\partial s)(rsin(t)sin(s))	\frac{\partial\:}{\partial\:s}(r\sin(t)\sin(s))
(\partial)/(\partial x)((4x-y)/(4x+y))	\frac{\partial\:}{\partial\:x}(\frac{4x-y}{4x+y})
(dy)/(dx)=y^{-1}x^{-3}	\frac{dy}{dx}=y^{-1}x^{-3}
y^'=(6y^2)/(x^2),y(-2)=5	y^{\prime\:}=\frac{6y^{2}}{x^{2}},y(-2)=5
derivative of 4/3 tan(x)	\frac{d}{dx}(\frac{4}{3}\tan(x))
limit as x approaches-1 of 13+x	\lim\:_{x\to\:-1}(13+x)
(dx)/(dt)=(x^2+tsqrt(t^2+x^2))/(tx)	\frac{dx}{dt}=\frac{x^{2}+t\sqrt{t^{2}+x^{2}}}{tx}
derivative of (x^2/(4+x))	\frac{d}{dx}(\frac{x^{2}}{4+x})
(\partial)/(\partial x)(-xy-x^2)	\frac{\partial\:}{\partial\:x}(-xy-x^{2})
derivative of 4x+3	derivative\:4x+3
integral of (cos(x))/(sin^{10)(x)}	\int\:\frac{\cos(x)}{\sin^{10}(x)}dx
integral of sqrt(4t^2+4)	\int\:\sqrt{4t^{2}+4}dt
integral of sin(2x+pi)	\int\:\sin(2x+π)dx
(dy}{dx}=\frac{e^x-y)/x	\frac{dy}{dx}=\frac{e^{x}-y}{x}
limit as x approaches 0 of xsin(1/x)	\lim\:_{x\to\:0}(x\sin(\frac{1}{x}))
maclaurin \sqrt[4]{1-x^4}	maclaurin\:\sqrt[4]{1-x^{4}}
derivative of-5t^2+75t-30	derivative\:-5t^{2}+75t-30
integral from 0 to 0 of 1	\int\:_{0}^{0}1
integral from 0 to 6 of (3-\|x-3\|)	\int\:_{0}^{6}(3-\left\|x-3\right\|)dx
derivative of e^x(4x^2-8x+8)	\frac{d}{dx}(e^{x}(4x^{2}-8x+8))
derivative of-4e^{-x}	\frac{d}{dx}(-4e^{-x})
integral from 1 to 2 of (10ln(x))/(x^2)	\int\:_{1}^{2}\frac{10\ln(x)}{x^{2}}dx
f(x)=arctan(5x)	f(x)=\arctan(5x)
integral from 1 to 2 of (x^2-3)	\int\:_{1}^{2}(x^{2}-3)dx
integral of ((x-1))/(sqrt((x^2-4x+3)))	\int\:\frac{(x-1)}{\sqrt{(x^{2}-4x+3)}}dx
derivative of (4x-7)/(x^2-1)	derivative\:\frac{4x-7}{x^{2}-1}
integral of 2sqrt(x+1)-2	\int\:2\sqrt{x+1}-2dx
integral of x/(sqrt(x-11))	\int\:\frac{x}{\sqrt{x-11}}dx
x^3+y^3=3xy^2(dy)/(dx)	x^{3}+y^{3}=3xy^{2}\frac{dy}{dx}
integral of e^{3x}sin(x)	\int\:e^{3x}\sin(x)dx
tangent of x^4-8x^3+7x^2-4,\at x=1	tangent\:x^{4}-8x^{3}+7x^{2}-4,\at\:x=1
derivative of f(x)=7e^e	derivative\:f(x)=7e^{e}
derivative of 5x^3+14x+23	\frac{d}{dx}(5x^{3}+14x+23)
factor e^{f(x)}	factor\:e^{f(x)}
yy^'=9cos(x)	yy^{\prime\:}=9\cos(x)
derivative of x/(12-(12)/x)	\frac{d}{dx}(\frac{x}{12}-\frac{12}{x})
(\partial)/(\partial x)((3x+6y)^{10})	\frac{\partial\:}{\partial\:x}((3x+6y)^{10})
integral of (sin(2x))/(23+cos^2(x))	\int\:\frac{\sin(2x)}{23+\cos^{2}(x)}dx
derivative of (1/(x-3)^2)	\frac{d}{dx}((\frac{1}{x-3})^{2})
derivative of f(x)=x-2cos(x)	derivative\:f(x)=x-2\cos(x)
derivative of (1-6t)/(3+t)	derivative\:\frac{1-6t}{3+t}
limit as x approaches 0+of 1/x+ln(x)	\lim\:_{x\to\:0+}(\frac{1}{x}+\ln(x))
(x^2+2y^2)dx=-xydy	(x^{2}+2y^{2})dx=-xydy
integral of xln(2x)	\int\:x\ln(2x)dx
derivative of (sec(x))/x	derivative\:\frac{\sec(x)}{x}
(dy)/(dx)=e^{x+y}	\frac{dy}{dx}=e^{x+y}

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