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Popular Calculus Problems

(\partial)/(\partial x)((3y)/(2x))	\frac{\partial\:}{\partial\:x}(\frac{3y}{2x})
derivative of f(x)=(x^2)/(7+sqrt(x))	derivative\:f(x)=\frac{x^{2}}{7+\sqrt{x}}
xy^'-2y=2yx^2	xy^{\prime\:}-2y=2yx^{2}
derivative of (x^2-3x^6(4-x)^5)	\frac{d}{dx}((x^{2}-3x)^{6}(4-x)^{5})
limit as x approaches 2 of e^{1/(x-2)}	\lim\:_{x\to\:2}(e^{\frac{1}{x-2}})
limit as x approaches 0 of x*cot(2x)	\lim\:_{x\to\:0}(x\cdot\:\cot(2x))
integral of (9-162x)/(sqrt(1-81x^2))	\int\:\frac{9-162x}{\sqrt{1-81x^{2}}}dx
derivative of y=a^5+cos^5(x)	derivative\:y=a^{5}+\cos^{5}(x)
derivative of (2x^{5/2}/5)	\frac{d}{dx}(\frac{2x^{\frac{5}{2}}}{5})
slope of y=x^2-2x-3,(2,-3)	slope\:y=x^{2}-2x-3,(2,-3)
(\partial)/(\partial x)(sqrt(xy))	\frac{\partial\:}{\partial\:x}(\sqrt{xy})
tangent of f(x)=x^4-4x^3+8,\at x=2	tangent\:f(x)=x^{4}-4x^{3}+8,\at\:x=2
integral of 2x^3-6x^2+2x-1+(2/x)	\int\:2x^{3}-6x^{2}+2x-1+(\frac{2}{x})dx
(\partial)/(\partial y)(sin(xy)+cos(xy))	\frac{\partial\:}{\partial\:y}(\sin(xy)+\cos(xy))
derivative of (x+1/(x^2-1))	\frac{d}{dx}(\frac{x+1}{x^{2}-1})
derivative of (x/(y^2)-(y/(x^2)))	\frac{d}{dx}((\frac{x}{y^{2}})-(\frac{y}{x^{2}}))
y^'+5y=4,y(0)=0	y^{\prime\:}+5y=4,y(0)=0
derivative of (8x^2+302x/(x-10))	\frac{d}{dx}(\frac{8x^{2}+302x}{x-10})
inverse oflaplace 1/(s+1)*1/s	inverselaplace\:\frac{1}{s+1}\cdot\:\frac{1}{s}
(\partial)/(\partial y)(y+e^x)	\frac{\partial\:}{\partial\:y}(y+e^{x})
sum from n=0 to infinity of n(1/4)^n	\sum\:_{n=0}^{\infty\:}n(\frac{1}{4})^{n}
integral of (e^x)/(3+5e^{2x)}	\int\:\frac{e^{x}}{3+5e^{2x}}dx
d/(dt)(cos(pit))	\frac{d}{dt}(\cos(πt))
(\partial)/(\partial x)(x^3-3xy^2+y^3)	\frac{\partial\:}{\partial\:x}(x^{3}-3xy^{2}+y^{3})
sum from n=1 to infinity of 7/n-7/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{7}{n}-\frac{7}{n+1}
limit as x approaches 0 of-6+6x^3	\lim\:_{x\to\:0}(-6+6x^{3})
sum from n=0 to infinity of x^n 1/(n!)	\sum\:_{n=0}^{\infty\:}x^{n}\frac{1}{n!}
y=3^2+3	y=3^{2}+3
area x^2-x,2x	area\:x^{2}-x,2x
derivative of x+sin(x)	derivative\:x+\sin(x)
integral of e^{2ax}	\int\:e^{2ax}dx
integral from-5 to 4 of t^2	\int\:_{-5}^{4}t^{2}dt
integral of ((sqrt(x^2-4)))/x	\int\:\frac{(\sqrt{x^{2}-4})}{x}dx
derivative of (8x^2+8x+8/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+8x+8}{\sqrt{x}})
derivative of x^3sinh^2(x+cosh^2(x^3))	\frac{d}{dx}(x^{3}\sinh^{2}(x)+\cosh^{2}(x^{3}))
integral of (x^3)/(sqrt(a^4+x^4))	\int\:\frac{x^{3}}{\sqrt{a^{4}+x^{4}}}dx
tangent of f(x)=-4-2x^2,\at x=-3	tangent\:f(x)=-4-2x^{2},\at\:x=-3
limit as x approaches infinity of xr^x	\lim\:_{x\to\:\infty\:}(xr^{x})
integral of (x+2)ln(x)	\int\:(x+2)\ln(x)dx
area x=9,x=y^2	area\:x=9,x=y^{2}
integral of 6/(t^2)	\int\:\frac{6}{t^{2}}dt
integral of 12x+12	\int\:12x+12dx
integral of (e^{4x}+4e^x+8)/(e^x)	\int\:\frac{e^{4x}+4e^{x}+8}{e^{x}}dx
derivative of cos^2(1-x)	\frac{d}{dx}(\cos^{2}(1-x))
inverse oflaplace 2/(s^2+40s+400)	inverselaplace\:\frac{2}{s^{2}+40s+400}
integral from 0 to 4 of e^{2x}	\int\:_{0}^{4}e^{2x}dx
simplify (ax^2+bx+c)*e^{-x/2}	simplify\:(ax^{2}+bx+c)\cdot\:e^{-\frac{x}{2}}
integral of x^5e^{-x}	\int\:x^{5}e^{-x}dx
tangent of f(x)= 5/x ,\at x=2	tangent\:f(x)=\frac{5}{x},\at\:x=2
derivative of sqrt(X)	derivative\:\sqrt{X}
(\partial)/(\partial x)(y(-2x-y+1))	\frac{\partial\:}{\partial\:x}(y(-2x-y+1))
derivative of e^{3x-1}	\frac{d}{dx}(e^{3x-1})
tangent of f(x)=(1-x)/(2x),\at x=1	tangent\:f(x)=\frac{1-x}{2x},\at\:x=1
derivative of 1/6 (x^2-4^{3/2})	\frac{d}{dx}(\frac{1}{6}(x^{2}-4)^{\frac{3}{2}})
integral of (5-50x)/(sqrt(49-25x^2))	\int\:\frac{5-50x}{\sqrt{49-25x^{2}}}dx
derivative of e^{2x}sqrt(x+1)	\frac{d}{dx}(e^{2x}\sqrt{x+1})
integral from 2 to infinity of ye^{-8y}	\int\:_{2}^{\infty\:}ye^{-8y}dy
derivative of cos^2(x^2+y^2)	\frac{d}{dx}(\cos^{2}(x^{2}+y^{2}))
integral from 2 to infinity of 8x^{-2}	\int\:_{2}^{\infty\:}8x^{-2}dx
integral of 7-1/(7x^2)	\int\:7-\frac{1}{7x^{2}}dx
limit as x approaches 0 of (1-e^x)^x	\lim\:_{x\to\:0}((1-e^{x})^{x})
integral of (x^6)/((8-x^7)^2)	\int\:\frac{x^{6}}{(8-x^{7})^{2}}dx
taylor 1/(x-1),6	taylor\:\frac{1}{x-1},6
limit as x approaches 0 of (e^x-1)/(18x)	\lim\:_{x\to\:0}(\frac{e^{x}-1}{18x})
derivative of x/(2x+sqrt(x)-3)	derivative\:\frac{x}{2x+\sqrt{x}-3}
integral of (inx)^2	\int\:(inx)^{2}dx
limit as x approaches infinity of 1+x	\lim\:_{x\to\:\infty\:}(1+x)
area y=2(x+1),y=3(x+1),x=5	area\:y=2(x+1),y=3(x+1),x=5
derivative of x^2+y^3	\frac{d}{dx}(x^{2}+y^{3})
y(dy)/(dx)=x-1	y\frac{dy}{dx}=x-1
derivative of 1/(5-5x^3)	derivative\:\frac{1}{5-5x^{3}}
integral of 19e^x	\int\:19e^{x}dx
limit as x approaches 1 of x^2-1	\lim\:_{x\to\:1}(x^{2}-1)
integral of e^xsin(x)x	\int\:e^{x}\sin(x)xdx
inverse oflaplace s/(s(s^2+s+1))	inverselaplace\:\frac{s}{s(s^{2}+s+1)}
integral of xcos^2(8x)	\int\:x\cos^{2}(8x)dx
(dy}{dx}=\frac{x+2)/y	\frac{dy}{dx}=\frac{x+2}{y}
integral of 1/(7x+3)	\int\:\frac{1}{7x+3}dx
d/(dt)((2t+7)/(2t))	\frac{d}{dt}(\frac{2t+7}{2t})
derivative of-2tan(x)	\frac{d}{dx}(-2\tan(x))
integral of (4x-1)^3	\int\:(4x-1)^{3}dx
integral from 1 to 6 of (2x^3+5x^2+2x+8)	\int\:_{1}^{6}(2x^{3}+5x^{2}+2x+8)dx
limit as x approaches 3+of 1/(6-2x)	\lim\:_{x\to\:3+}(\frac{1}{6-2x})
tangent of f(x)=1.1x+e^x,\at x=0	tangent\:f(x)=1.1x+e^{x},\at\:x=0
integral of (x^2)/(x^4-6x^2-27)	\int\:\frac{x^{2}}{x^{4}-6x^{2}-27}dx
yy^'+36x=0	yy^{\prime\:}+36x=0
derivative of (8x^2-16x+16e^x)	\frac{d}{dx}((8x^{2}-16x+16)e^{x})
integral of (20x^3-40x^2+9)/(x^2-2x)	\int\:\frac{20x^{3}-40x^{2}+9}{x^{2}-2x}dx
(\partial)/(\partial x)((2x+1)^2)	\frac{\partial\:}{\partial\:x}((2x+1)^{2})
derivative of 4x^2	\frac{d}{dx}(4x^{2})
(\partial)/(\partial z)(e^x)	\frac{\partial\:}{\partial\:z}(e^{x})
derivative of x^25e^x	\frac{d}{dx}(x^{2}5e^{x})
y^3-(6x+2)+3xy^2y^'=0	y^{3}-(6x+2)+3xy^{2}y^{\prime\:}=0
tangent of (x^3-4x)^8	tangent\:(x^{3}-4x)^{8}
integral of xcos^2(x)	\int\:x\cos^{2}(x)dx
(\partial)/(\partial x)(sqrt(x^2+y^2-1))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}-1})
derivative of sec(2xtan(2x))	\frac{d}{dx}(\sec(2x)\tan(2x))
(\partial)/(\partial x)(x-z-arctan(yz))	\frac{\partial\:}{\partial\:x}(x-z-\arctan(yz))
derivative of f(x)=(x^3)/((x^2+4)^2)	derivative\:f(x)=\frac{x^{3}}{(x^{2}+4)^{2}}
derivative of (cos(x)/x)	\frac{d}{dx}(\frac{\cos(x)}{x})

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