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Popular Calculus Problems

derivative of (2x^3-1/(x^2))	\frac{d}{dx}(\frac{2x^{3}-1}{x^{2}})
derivative of x(2x+1^{1/3})	\frac{d}{dx}(x(2x+1)^{\frac{1}{3}})
integral of 1/((x+4))	\int\:\frac{1}{(x+4)}dx
(dy)/(dx)=((x^2y-y))/(y+1)	\frac{dy}{dx}=\frac{(x^{2}y-y)}{y+1}
laplacetransform sin((2t)/3)	laplacetransform\:\sin(\frac{2t}{3})
derivative of 934+20x-0.079x^2	derivative\:934+20x-0.079x^{2}
derivative of x/((x-7^2))	\frac{d}{dx}(\frac{x}{(x-7)^{2}})
inverse oflaplace (6s-5)/(s^2+7)	inverselaplace\:\frac{6s-5}{s^{2}+7}
y^'-(2y)/x =x^3y^{-3}	y^{\prime\:}-\frac{2y}{x}=x^{3}y^{-3}
derivative of x^2+log_{2}(x^2+4)	\frac{d}{dx}(x^{2}+\log_{2}(x^{2}+4))
derivative of-e^{-x}x	\frac{d}{dx}(-e^{-x}x)
factor t^3+t	factor\:t^{3}+t
y^'=2sec^2(x)e^{2y}	y^{\prime\:}=2\sec^{2}(x)e^{2y}
derivative of (sqrt(x)-5/(sqrt(x)+5))	\frac{d}{dx}(\frac{\sqrt{x}-5}{\sqrt{x}+5})
ycos(xy)-tan(x)+xcos(xy)y^'=0	y\cos(xy)-\tan(x)+x\cos(xy)y^{\prime\:}=0
slope of (7,14),(9,18)	slope\:(7,14),(9,18)
tangent of f(x)=2x^3-8x,(2,0)	tangent\:f(x)=2x^{3}-8x,(2,0)
maclaurin x-sin(x)	maclaurin\:x-\sin(x)
derivative of ln(sin(10x))	\frac{d}{dx}(\ln(\sin(10x)))
y^{''}+6y^'-16y=-272sin(8x)	y^{\prime\:\prime\:}+6y^{\prime\:}-16y=-272\sin(8x)
derivative of (ln(cos(2x))/x)	\frac{d}{dx}(\frac{\ln(\cos(2x))}{x})
derivative of 2xe^{-4x}	\frac{d}{dx}(2xe^{-4x})
tangent of y=sin(3x)+cos(8x)	tangent\:y=\sin(3x)+\cos(8x)
derivative of cos(sqrt(3)x)	\frac{d}{dx}(\cos(\sqrt{3}x))
derivative of arcsin(x+arccos(x))	\frac{d}{dx}(\arcsin(x)+\arccos(x))
limit as x approaches 2-of 2x	\lim\:_{x\to\:2-}(2x)
integral of sqrt(8x+1)	\int\:\sqrt{8x+1}dx
derivative of 3x^2+4x-4	\frac{d}{dx}(3x^{2}+4x-4)
sum from n=2 to infinity of 1/(2^n-1)	\sum\:_{n=2}^{\infty\:}\frac{1}{2^{n}-1}
integral of (e^t+1)^2	\int\:(e^{t}+1)^{2}dt
limit as x approaches 2 of 1/(x+1)	\lim\:_{x\to\:2}(\frac{1}{x+1})
integral of (sec^2(6x))/(tan(6x)+2)	\int\:\frac{\sec^{2}(6x)}{\tan(6x)+2}dx
inverse oflaplace (3s)/(s^2+3s+16)	inverselaplace\:\frac{3s}{s^{2}+3s+16}
derivative of x^3tan(x)	\frac{d}{dx}(x^{3}\tan(x))
integral of 1/(5sqrt(x)(2+\sqrt{x))}	\int\:\frac{1}{5\sqrt{x}(2+\sqrt{x})}dx
(\partial)/(\partial x)(e^{x+y+4})	\frac{\partial\:}{\partial\:x}(e^{x+y+4})
limit as x approaches 5 of sqrt(x-5)	\lim\:_{x\to\:5}(\sqrt{x-5})
derivative of f(x)=x^3-2x^2	derivative\:f(x)=x^{3}-2x^{2}
limit as x approaches 1 of sqrt(5x+4)	\lim\:_{x\to\:1}(\sqrt{5x+4})
derivative of k^2+7x+10	derivative\:k^{2}+7x+10
integral from 0 to pi of cos(x)sin^2(x)	\int\:_{0}^{π}\cos(x)\sin^{2}(x)dx
integral from-1 to 1 of xsin(pix)	\int\:_{-1}^{1}x\sin(πx)dx
integral of 2/u	\int\:\frac{2}{u}du
y^{''}-12y^'+52y=0	y^{\prime\:\prime\:}-12y^{\prime\:}+52y=0
integral from 0 to 1 of (1-x)^9	\int\:_{0}^{1}(1-x)^{9}dx
derivative of f(x)=sqrt(7x+9)	derivative\:f(x)=\sqrt{7x+9}
derivative of f(x)=18x^2-27x	derivative\:f(x)=18x^{2}-27x
(\partial)/(\partial x)((x^3-y^2)^2)	\frac{\partial\:}{\partial\:x}((x^{3}-y^{2})^{2})
(\partial)/(\partial x)((x+y)^5)	\frac{\partial\:}{\partial\:x}((x+y)^{5})
area y=1-x^2,y=x-1	area\:y=1-x^{2},y=x-1
integral of 3sin(x	\int\:3\sin(d)xdx
integral from-1 to 3 of (-x)^3	\int\:_{-1}^{3}(-x)^{3}dx
derivative of g(x)=x^2(1-6x)	derivative\:g(x)=x^{2}(1-6x)
integral of x(4-x)^2	\int\:x(4-x)^{2}dx
derivative of 14xsin(x)	\frac{d}{dx}(14x\sin(x))
derivative of (-2x+y/(-x+2y))	\frac{d}{dx}(\frac{-2x+y}{-x+2y})
derivative of (7x^6+2x^3^4)	\frac{d}{dx}((7x^{6}+2x^{3})^{4})
derivative of ln(169sin^2(x))	derivative\:\ln(169\sin^{2}(x))
factor 2cos(4x)+2e^{-0.2x}	factor\:2\cos(4x)+2e^{-0.2x}
derivative of 2^{sin(pix)}	derivative\:2^{\sin(πx)}
(\partial)/(\partial x)(x/(x^2+x+1))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+x+1})
derivative of ((6x^2)/(6-x))^3	derivative\:(\frac{6x^{2}}{6-x})^{3}
integral of ((1-x)y)/x	\int\:\frac{(1-x)y}{x}
limit as x approaches 0 of \|5x\|	\lim\:_{x\to\:0}(\left\|5x\right\|)
derivative of 1/(\sqrt[3]{2x-1})	\frac{d}{dx}(\frac{1}{\sqrt[3]{2x-1}})
derivative of xln(ln(x))	\frac{d}{dx}(x\ln(\ln(x)))
integral of (x^2+1)/((x+2)(x^2+2x+5))	\int\:\frac{x^{2}+1}{(x+2)(x^{2}+2x+5)}dx
implicit (dy)/(dx),2xy=5	implicit\:\frac{dy}{dx},2xy=5
y^'=(x^2e^{y/x}+y^2)/(xy)	y^{\prime\:}=\frac{x^{2}e^{\frac{y}{x}}+y^{2}}{xy}
derivative of (x-4(ln(x/4)))	\frac{d}{dx}((x-4)(\ln(\frac{x}{4})))
derivative of f(x)=(e^x)/(7x^2+4)	derivative\:f(x)=\frac{e^{x}}{7x^{2}+4}
tangent of 8x-8sqrt(x)	tangent\:8x-8\sqrt{x}
integral from 0.5 to 3 of (sin(x))/x	\int\:_{0.5}^{3}\frac{\sin(x)}{x}dx
laplacetransform t-3	laplacetransform\:t-3
tangent of y=-4cos(x),\at x= pi/2	tangent\:y=-4\cos(x),\at\:x=\frac{π}{2}
integral of (x+6)(x-3)	\int\:(x+6)(x-3)dx
(\partial)/(\partial x)(x*sqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(x\cdot\:\sqrt{x^{2}+y^{2}})
limit as x approaches 0 of (1-5x)^{2/x}	\lim\:_{x\to\:0}((1-5x)^{\frac{2}{x}})
(\partial)/(\partial y)(x^2y^2e^{y^2})	\frac{\partial\:}{\partial\:y}(x^{2}y^{2}e^{y^{2}})
sum from n=0 to infinity of (-1/5)^n	\sum\:_{n=0}^{\infty\:}(-\frac{1}{5})^{n}
derivative of 1/(x 3/2)	\frac{d}{dx}(\frac{1}{x\frac{3}{2}})
(te^{-t})^'	(te^{-t})^{\prime\:}
(\partial)/(\partial x)(rcos(t))	\frac{\partial\:}{\partial\:x}(r\cos(t))
(dy)/(dx)= 1/x (y^2+0.8y),y(1)=0.7	\frac{dy}{dx}=\frac{1}{x}(y^{2}+0.8y),y(1)=0.7
derivative of 18x+ln(18x)	\frac{d}{dx}(18x+\ln(18x))
sum from n=0 to infinity of n/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{n}{4^{n}}
integral of sin(6x)cos(4x)	\int\:\sin(6x)\cos(4x)dx
integral of x^3	\int\:x^{3}dx
derivative of-4x^2+2x-3	\frac{d}{dx}(-4x^{2}+2x-3)
derivative of-2x^4(4x^2+1)^3	derivative\:-2x^{4}(4x^{2}+1)^{3}
limit as t approaches 0 of (e^{2t})/(sin(t))	\lim\:_{t\to\:0}(\frac{e^{2t}}{\sin(t)})
integral of ((x+1))/(7x+x^2)	\int\:\frac{(x+1)}{7x+x^{2}}dx
slope of (1.2)(4.4)	slope\:(1.2)(4.4)
sum from n=0 to infinity of (7^n)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{7^{n}}{n!}
lcm ln(2x),0,2	lcm\:\ln(2x),0,2
derivative of (3^{2x}/x)	\frac{d}{dx}(\frac{3^{2x}}{x})
limit as x approaches 0 of (1+2x)^{4/x}	\lim\:_{x\to\:0}((1+2x)^{\frac{4}{x}})
integral of (x^3+x+5)/(x^2+1)	\int\:\frac{x^{3}+x+5}{x^{2}+1}dx
(dN)/(dt)=N(1-0.001N)	\frac{dN}{dt}=N(1-0.001N)
integral of ((arctan(x))^8)/(x^2+1)	\int\:\frac{(\arctan(x))^{8}}{x^{2}+1}dx

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