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Popular Calculus Problems

tangent of y=(x^2)/(x+5),(1, 1/6)	tangent\:y=\frac{x^{2}}{x+5},(1,\frac{1}{6})
(\partial)/(\partial x)(1/x+1/(y+z))	\frac{\partial\:}{\partial\:x}(\frac{1}{x}+\frac{1}{y+z})
(\partial)/(\partial x)(yx^2z^2-xy^4+xz)	\frac{\partial\:}{\partial\:x}(yx^{2}z^{2}-xy^{4}+xz)
derivative of (3x^2+5x+1^{3/2})	\frac{d}{dx}((3x^{2}+5x+1)^{\frac{3}{2}})
derivative of f(x)=log_{41}(2x-4)	derivative\:f(x)=\log_{41}(2x-4)
derivative of ln(xcos(x))	\frac{d}{dx}(\ln(x)\cos(x))
x^2y^{''}+3xy^'-15y=0	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}-15y=0
inverse oflaplace 6/(s^2+5s+6)	inverselaplace\:\frac{6}{s^{2}+5s+6}
limit as x approaches 4 of (x^2+x)/(x+1)	\lim\:_{x\to\:4}(\frac{x^{2}+x}{x+1})
area y=17-x^2,x=0,y=0	area\:y=17-x^{2},x=0,y=0
integral of ((x^2-1))/((x^2+1))	\int\:\frac{(x^{2}-1)}{(x^{2}+1)}dx
(\partial)/(\partial x)(2xe^y)	\frac{\partial\:}{\partial\:x}(2xe^{y})
tangent of 1/x ,\at x=3	tangent\:\frac{1}{x},\at\:x=3
tangent of 5sin^2(x^2)	tangent\:5\sin^{2}(x^{2})
integral of 1/(xsin^2(ln(x)))	\int\:\frac{1}{x\sin^{2}(\ln(x))}dx
integral from 0 to 5 of (5t)/((t-6)^2)	\int\:_{0}^{5}\frac{5t}{(t-6)^{2}}dt
limit as x approaches 1 of 2x	\lim\:_{x\to\:1}(2x)
derivative of ax^{-2}	\frac{d}{dx}(ax^{-2})
tangent of y=((x+3))/((x+1)^2),\at x=0	tangent\:y=\frac{(x+3)}{(x+1)^{2}},\at\:x=0
(\partial)/(\partial x)(3e^x-5xe^y)	\frac{\partial\:}{\partial\:x}(3e^{x}-5xe^{y})
derivative of 2/(1+3e^{-2x})	\frac{d}{dx}(\frac{2}{1+3e^{-2x}})
derivative of y=sin(cos(tan(pix)))	derivative\:y=\sin(\cos(\tan(πx)))
sum from n=1 to infinity of (4^n)/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{4^{n}}{7^{n}}
derivative of 0.006x^3+0.07x^2+18x+600	\frac{d}{dx}(0.006x^{3}+0.07x^{2}+18x+600)
integral from-infinity to infinity of (2x)/((x^2+1)^{12)}	\int\:_{-\infty\:}^{\infty\:}\frac{2x}{(x^{2}+1)^{12}}dx
(dy)/(dx)=y(2x-5)	\frac{dy}{dx}=y(2x-5)
limit as x approaches 4 of (x^2-8x+16)/(x-4)	\lim\:_{x\to\:4}(\frac{x^{2}-8x+16}{x-4})
derivative of cos(5x)	derivative\:\cos(5x)
derivative of (sqrt(x)/(e^x))	\frac{d}{dx}(\frac{\sqrt{x}}{e^{x}})
y^'+2y=6e^x	y^{\prime\:}+2y=6e^{x}
(dy)/(dx)=xe^{-y}+10e^{-y}	\frac{dy}{dx}=xe^{-y}+10e^{-y}
integral of (14x)/(sqrt(1-x^4))	\int\:\frac{14x}{\sqrt{1-x^{4}}}dx
(\partial)/(\partial x)(xy)	\frac{\partial\:}{\partial\:x}(xy)
(\partial)/(\partial t)(10e^{-0.25x}sin((2pi)/(365)t-0.25x))	\frac{\partial\:}{\partial\:t}(10e^{-0.25x}\sin(\frac{2π}{365}t-0.25x))
integral of cos(5x)sin(x)	\int\:\cos(5x)\sin(x)dx
derivative of ((e^x/(x^e))^2)	\frac{d}{dx}((\frac{e^{x}}{x^{e}})^{2})
integral of (x^4+x^2+25)/(5x^4(x^2+25))	\int\:\frac{x^{4}+x^{2}+25}{5x^{4}(x^{2}+25)}dx
(\partial)/(\partial x)(2xy(x+y)+x^2+2x)	\frac{\partial\:}{\partial\:x}(2xy(x+y)+x^{2}+2x)
(\partial)/(\partial y)(ln(x^2y))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}y))
derivative of 7*ln(x)	derivative\:7\cdot\:\ln(x)
derivative of sin^3(3x)	derivative\:\sin^{3}(3x)
(\partial)/(\partial y)(-2cos(y))	\frac{\partial\:}{\partial\:y}(-2\cos(y))
(\partial)/(\partial x)(sqrt(x^4-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{4}-y^{2}})
derivative of (x^2+1/(x^2-3))	\frac{d}{dx}(\frac{x^{2}+1}{x^{2}-3})
derivative of f(x)=cos^3(x)	derivative\:f(x)=\cos^{3}(x)
simplify ln(1/x)	simplify\:\ln(\frac{1}{x})
integral of e^{3x+2}	\int\:e^{3x+2}dx
derivative of ln^2(x^2)	derivative\:\ln^{2}(x^{2})
integral from 0 to 14 of 2pix(14x-x^2)	\int\:_{0}^{14}2πx(14x-x^{2})dx
derivative of e^{x^2+3}	\frac{d}{dx}(e^{x^{2}+3})
derivative of-(2x/(x^2+1))	\frac{d}{dx}(-\frac{2x}{x^{2}+1})
integral of 1/(2y+y^2)	\int\:\frac{1}{2y+y^{2}}dy
integral from 0 to 0.6 of 750x	\int\:_{0}^{0.6}750xdx
(\partial)/(\partial x)(2x^4y+sin(x^3))	\frac{\partial\:}{\partial\:x}(2x^{4}y+\sin(x^{3}))
integral from 0 to 3pi of 5x^2sin(1/6 x)	\int\:_{0}^{3π}5x^{2}\sin(\frac{1}{6}x)dx
area \|sqrt(x+4)-2\|,\|sqrt(16-x)\|,0,16	area\:\left\|\sqrt{x+4}-2\right\|,\left\|\sqrt{16-x}\right\|,0,16
integral from 0 to 1 of (11)/(4y-1)	\int\:_{0}^{1}\frac{11}{4y-1}dy
sum from n=1 to infinity}(\sqrt{n of)/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{\sqrt{n}}{n^{2}}
integral from 0 to 1 of ln(3x)	\int\:_{0}^{1}\ln(3x)dx
integral of (2x)/((2+3x^2)^3)	\int\:\frac{2x}{(2+3x^{2})^{3}}dx
integral from 0 to 4 of 1/(x^2+16)	\int\:_{0}^{4}\frac{1}{x^{2}+16}dx
derivative of (sqrt(x))/(4+x)	derivative\:\frac{\sqrt{x}}{4+x}
(\partial)/(\partial x)(xy+xe^{y/x})	\frac{\partial\:}{\partial\:x}(xy+xe^{\frac{y}{x}})
integral of 8te^t	\int\:8te^{t}dt
4(dy)/(dx)+20y=5	4\frac{dy}{dx}+20y=5
integral of 2/(-x)	\int\:\frac{2}{-x}dx
derivative of 2csc(2x)	\frac{d}{dx}(2\csc(2x))
(\partial)/(\partial y)(sin(x*y))	\frac{\partial\:}{\partial\:y}(\sin(x\cdot\:y))
derivative of (2x^2-3)^3	derivative\:(2x^{2}-3)^{3}
laplacetransform 8t^2	laplacetransform\:8t^{2}
y^'+2y=60,y(1)=80	y^{\prime\:}+2y=60,y(1)=80
(dy}{dx}+\frac{3y)/x =x^5y^3	\frac{dy}{dx}+\frac{3y}{x}=x^{5}y^{3}
2xy^2+x^2y^'=y^2	2xy^{2}+x^{2}y^{\prime\:}=y^{2}
y^'=y(3-y),y(0)=5	y^{\prime\:}=y(3-y),y(0)=5
derivative of f(x)=sqrt(3)sin(x)+cos(x)	derivative\:f(x)=\sqrt{3}\sin(x)+\cos(x)
limit as x approaches-infinity of x,-2	\lim\:_{x\to\:-\infty\:}(x,-2)
integral of (-4)/((3x)^3)	\int\:\frac{-4}{(3x)^{3}}dx
y^'=(x^2+y^2)/(xy)	y^{\prime\:}=\frac{x^{2}+y^{2}}{xy}
(\partial)/(\partial x)(x+3y)	\frac{\partial\:}{\partial\:x}(x+3y)
integral of (3x^2+2x)ln(x)	\int\:(3x^{2}+2x)\ln(x)dx
(x^2+y^2+1)dx+x(x-2y)dy=0	(x^{2}+y^{2}+1)dx+x(x-2y)dy=0
derivative of (1+sin(3x)^4)	\frac{d}{dx}((1+\sin(3x))^{4})
derivative of (3cos(2x+sin(3x)+4)^2)	\frac{d}{dx}((3\cos(2x)+\sin(3x)+4)^{2})
y^'-4y=10sin(2t),y(0)=0	y^{\prime\:}-4y=10\sin(2t),y(0)=0
derivative of f(x)=-3/(e^{3x)}	derivative\:f(x)=-\frac{3}{e^{3x}}
limit as x approaches-3 of x^2+4x+1	\lim\:_{x\to\:-3}(x^{2}+4x+1)
integral of 1/(x(4-x))	\int\:\frac{1}{x(4-x)}dx
(\partial)/(\partial y)(ye^{2xy}+x)	\frac{\partial\:}{\partial\:y}(ye^{2xy}+x)
integral of X	\int\:XdX
integral of x/(sqrt(2x^2+3))	\int\:\frac{x}{\sqrt{2x^{2}+3}}dx
derivative of e^x-2e^{-2x}	\frac{d}{dx}(e^{x}-2e^{-2x})
area-x^2+3x,0	area\:-x^{2}+3x,0
x^2(dy)/(dx)-2xy=4y^4,y(1)= 1/2	x^{2}\frac{dy}{dx}-2xy=4y^{4},y(1)=\frac{1}{2}
(\partial)/(\partial x)(-cos(x))	\frac{\partial\:}{\partial\:x}(-\cos(x))
limit as x approaches-8 of (\sqrt[3]{x}+2)/(x+8)	\lim\:_{x\to\:-8}(\frac{\sqrt[3]{x}+2}{x+8})
integral of (x^2+3x+7)/(sqrt(x))	\int\:\frac{x^{2}+3x+7}{\sqrt{x}}dx
derivative of y=5x^2e^{2x}	derivative\:y=5x^{2}e^{2x}
derivative of y=4*5^x	derivative\:y=4\cdot\:5^{x}
derivative of (x(x^2-1)/(sqrt(x^2+1)))	\frac{d}{dx}(\frac{x(x^{2}-1)}{\sqrt{x^{2}+1}})
limit as x approaches 0 of x^2(sin(1/x))	\lim\:_{x\to\:0}(x^{2}(\sin(\frac{1}{x})))

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