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Popular Calculus Problems

limit as x approaches 0 of (sinh(x))/x	\lim\:_{x\to\:0}(\frac{\sinh(x)}{x})
derivative of (6x^2+2x+4)/(sqrt(x))	derivative\:\frac{6x^{2}+2x+4}{\sqrt{x}}
y^{''}+3y^'-2y=0	y^{\prime\:\prime\:}+3y^{\prime\:}-2y=0
(dy)/(dx)=4e^{x-y}	\frac{dy}{dx}=4e^{x-y}
(xy+y^2+y)dx+(x+2y)dy=0	(xy+y^{2}+y)dx+(x+2y)dy=0
y^'=cos(x+y)	y^{\prime\:}=\cos(x+y)
(\partial)/(\partial x)(e^xcos(x+y))	\frac{\partial\:}{\partial\:x}(e^{x}\cos(x+y))
derivative of sec(pi/3)	derivative\:\sec(\frac{π}{3})
integral of sec^4(x/4)	\int\:\sec^{4}(\frac{x}{4})dx
derivative of 5/((x-6^2))	\frac{d}{dx}(\frac{5}{(x-6)^{2}})
integral from 1/5 to 3 of 8xln(5x)	\int\:_{\frac{1}{5}}^{3}8x\ln(5x)dx
derivative of ln(e)	derivative\:\ln(e)
integral of x^{3/4}	\int\:x^{\frac{3}{4}}dx
y^{''}+289y=sec(17x)	y^{\prime\:\prime\:}+289y=\sec(17x)
derivative of f(x)=2x^5-3e^{6x}	derivative\:f(x)=2x^{5}-3e^{6x}
integral from 0 to 1 of x^2-sqrt(x)	\int\:_{0}^{1}x^{2}-\sqrt{x}dx
tangent of-2x^5+4x^4	tangent\:-2x^{5}+4x^{4}
derivative of (12/x-4/(x^3)+1/(x^4))	\frac{d}{dx}(\frac{12}{x}-\frac{4}{x^{3}}+\frac{1}{x^{4}})
y^{''}+2y^'+y=0,y(2)=1,y^'(2)=-2	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(2)=1,y^{\prime\:}(2)=-2
integral of ((x^2-x+1))/((x^2+x))	\int\:\frac{(x^{2}-x+1)}{(x^{2}+x)}dx
derivative of 11sqrt(x)-6/x	\frac{d}{dx}(11\sqrt{x}-\frac{6}{x})
integral of t^6e^{-t^7}	\int\:t^{6}e^{-t^{7}}dt
integral of 1/(v^2-1)	\int\:\frac{1}{v^{2}-1}dv
derivative of ln(sqrt(x)-1)	\frac{d}{dx}(\ln(\sqrt{x}-1))
integral of 1/(sqrt(x)(1-2\sqrt{x))}	\int\:\frac{1}{\sqrt{x}(1-2\sqrt{x})}dx
derivative of y= 7/(ln(x))	derivative\:y=\frac{7}{\ln(x)}
derivative of (5x/6)	\frac{d}{dx}(\frac{5x}{6})
limit as x approaches 9-of 1/(x-9)	\lim\:_{x\to\:9-}(\frac{1}{x-9})
limit as x approaches 0+of x[ln(x)]^2	\lim\:_{x\to\:0+}(x[\ln(x)]^{2})
derivative of 2^{5x}3^{4x^2}	\frac{d}{dx}(2^{5x}3^{4x^{2}})
(dy)/(dx)=(x-4)/(y+5)	\frac{dy}{dx}=\frac{x-4}{y+5}
tangent of f(x)= 2/x ,(6, 1/3)	tangent\:f(x)=\frac{2}{x},(6,\frac{1}{3})
integral of 15ln(x+5)	\int\:15\ln(x+5)dx
derivative of 7e^x+8/(\sqrt[3]{x)}	derivative\:7e^{x}+\frac{8}{\sqrt[3]{x}}
integral of (x^2+5x-1)/(x^3)	\int\:\frac{x^{2}+5x-1}{x^{3}}dx
integral of (-3x+2)e-x	\int\:(-3x+2)e-xdx
limit as x approaches 1 of (\sqrt[4]{x}-1)/(\sqrt[5]{x)-1}	\lim\:_{x\to\:1}(\frac{\sqrt[4]{x}-1}{\sqrt[5]{x}-1})
limit as x approaches 3 of ((x^{2-7x+12}))/((3-x))	\lim\:_{x\to\:3}(\frac{(x^{2-7x+12})}{(3-x)})
integral of y/((y+1)^2)	\int\:\frac{y}{(y+1)^{2}}dy
limit as x approaches infinity of-2xe^{-2x}	\lim\:_{x\to\:\infty\:}(-2xe^{-2x})
derivative of y= 1/(2cos^2(x))	derivative\:y=\frac{1}{2\cos^{2}(x)}
sum from i=0 to infinity of i/(2^i)	\sum\:_{i=0}^{\infty\:}\frac{i}{2^{i}}
(dy}{dx}=\frac{x^3)/y	\frac{dy}{dx}=\frac{x^{3}}{y}
integral of x/((x+1)^8)	\int\:\frac{x}{(x+1)^{8}}dx
integral of (e^{5x})/(e^{5x)+4}	\int\:\frac{e^{5x}}{e^{5x}+4}dx
(\partial)/(\partial y)(pix^2y)	\frac{\partial\:}{\partial\:y}(πx^{2}y)
integral of 21x^2ln(x)	\int\:21x^{2}\ln(x)dx
(dy)/(dt)=te^{2y}	\frac{dy}{dt}=te^{2y}
integral of xln(3x^2)	\int\:x\ln(3x^{2})dx
1/x dx+dy=0	\frac{1}{x}dx+dy=0
derivative of arctan(e^{4x})	derivative\:\arctan(e^{4x})
derivative of-5/(\sqrt[3]{x)}	derivative\:-\frac{5}{\sqrt[3]{x}}
derivative of arccos(4x^9)	derivative\:\arccos(4x^{9})
derivative of y=(x^3)/(1-x^2)	derivative\:y=\frac{x^{3}}{1-x^{2}}
xdx=ydy	xdx=ydy
limit as x approaches infinity+of 1/(sqrt(x^2+x))	\lim\:_{x\to\:\infty\:+}(\frac{1}{\sqrt{x^{2}+x}})
integral of sqrt(1+(3x^{1/2))^2}	\int\:\sqrt{1+(3x^{\frac{1}{2}})^{2}}dx
integral from 1/5 to 7 of 16xln(5x)	\int\:_{\frac{1}{5}}^{7}16x\ln(5x)dx
integral from 2 to 4 of (x^2+4)^3x	\int\:_{2}^{4}(x^{2}+4)^{3}xdx
derivative of (ln(3x+1)/(6x+2))	\frac{d}{dx}(\frac{\ln(3x+1)}{6x+2})
tangent of 9/(sin(x)+cos(x))	tangent\:\frac{9}{\sin(x)+\cos(x)}
area x,3x,4-x	area\:x,3x,4-x
integral of sqrt(4-y^2)	\int\:\sqrt{4-y^{2}}dy
integral from 0 to 1 of 1/(sqrt(x(1-x)))	\int\:_{0}^{1}\frac{1}{\sqrt{x(1-x)}}dx
slope ofintercept (7.4)(9.8)	slopeintercept\:(7.4)(9.8)
integral of-sin(ln(x))ln(x)	\int\:-\sin(\ln(x))\ln(x)dx
x*(dy)/(dx)+4y=1	x\cdot\:\frac{dy}{dx}+4y=1
x(dy)/(dx)+(2x+1)/(x+1)y=x-1	x\frac{dy}{dx}+\frac{2x+1}{x+1}y=x-1
taylor 1/(1-1/x),0	taylor\:\frac{1}{1-\frac{1}{x}},0
integral of 1/((b^2-x^2)^{3/2)}	\int\:\frac{1}{(b^{2}-x^{2})^{\frac{3}{2}}}dx
derivative of f(x)=10x^2+10x+8+ln(x)	derivative\:f(x)=10x^{2}+10x+8+\ln(x)
y^{''}+9y=cos(6t)	y^{\prime\:\prime\:}+9y=\cos(6t)
limit as x approaches 2-of 2	\lim\:_{x\to\:2-}(2)
tangent of y=arctan(-2x),\at x=-3	tangent\:y=\arctan(-2x),\at\:x=-3
integral of 14e^x	\int\:14e^{x}dx
tangent of f(x)=1-6x^2,(2,-23)	tangent\:f(x)=1-6x^{2},(2,-23)
(\partial)/(\partial x)(xy+y^2)	\frac{\partial\:}{\partial\:x}(xy+y^{2})
tangent of x^3+y^3-9xy=0,(4,2)	tangent\:x^{3}+y^{3}-9xy=0,(4,2)
integral of xe^{-x^3}	\int\:xe^{-x^{3}}dx
integral of ((4x^m-3x^n)^3)/(sqrt(x))	\int\:\frac{(4x^{m}-3x^{n})^{3}}{\sqrt{x}}dx
limit as x approaches infinity of (-1)^{-x}	\lim\:_{x\to\:\infty\:}((-1)^{-x})
integral of (x^4-x^2+1/(4x^3)-1/(x^2))	\int\:(x^{4}-x^{2}+\frac{1}{4x^{3}}-\frac{1}{x^{2}})dx
inverse oflaplace 3/((s^2+4))	inverselaplace\:\frac{3}{(s^{2}+4)}
derivative of 27n+3q^2n	derivative\:27n+3q^{2}n
derivative of y=(4x-1)/(2x+5)	derivative\:y=\frac{4x-1}{2x+5}
derivative of sin(x^3cos(x^2))	\frac{d}{dx}(\sin(x^{3})\cos(x^{2}))
(dy)/(dx)=x^2-y-2,y(0)=-1	\frac{dy}{dx}=x^{2}-y-2,y(0)=-1
integral from 0 to 5 of 9800pi(5-y)	\int\:_{0}^{5}9800π(5-y)dy
integral of (sin(x)cos^3(x))	\int\:(\sin(x)\cos^{3}(x))dx
limit as x approaches infinity of ((2x-1)(3-x))/((x-1)(x+3))	\lim\:_{x\to\:\infty\:}(\frac{(2x-1)(3-x)}{(x-1)(x+3)})
y^'=(2x^4e^{y/x}+x^2y^2)/(x^3y)	y^{\prime\:}=\frac{2x^{4}e^{\frac{y}{x}}+x^{2}y^{2}}{x^{3}y}
integral of-(sin(2x))/4	\int\:-\frac{\sin(2x)}{4}dx
y^{''}+y^'+y=cos(t)	y^{\prime\:\prime\:}+y^{\prime\:}+y=\cos(t)
integral of (7x^6+2)/(x^7+2x)	\int\:\frac{7x^{6}+2}{x^{7}+2x}dx
tangent of 2x^2	tangent\:2x^{2}
integral from-2 to-1 of (u-1/(u^2))	\int\:_{-2}^{-1}(u-\frac{1}{u^{2}})du
derivative of sqrt(1+x^2)	derivative\:\sqrt{1+x^{2}}
(dy)/(dx)=e^{2x}(1+y^2)	\frac{dy}{dx}=e^{2x}(1+y^{2})
derivative of y=3x^2+5	derivative\:y=3x^{2}+5
integral of 2/(5cos^2(x))	\int\:\frac{2}{5\cos^{2}(x)}dx

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