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Popular Calculus Problems

y^'=e^{-2x}	y^{\prime\:}=e^{-2x}
derivative of 26e^{x^2}x	derivative\:26e^{x^{2}}x
tangent of f(x)=x^2+1	tangent\:f(x)=x^{2}+1
7y^{''}+5y^'+7y=0	7y^{\prime\:\prime\:}+5y^{\prime\:}+7y=0
limit as h approaches 0 of (4/(2+h)-2)/h	\lim\:_{h\to\:0}(\frac{\frac{4}{2+h}-2}{h})
area x=1-y^2,-x-1	area\:x=1-y^{2},-x-1
derivative of sqrt(2{p)(xx})	\frac{d}{dx}(\sqrt{2{p}(x)x})
derivative of arctan(x/3)	derivative\:\arctan(\frac{x}{3})
derivative of f(x)=x+sqrt(x)+2	derivative\:f(x)=x+\sqrt{x}+2
(\partial)/(\partial x)(xy(x-2)(y+3))	\frac{\partial\:}{\partial\:x}(xy(x-2)(y+3))
integral of xln(x+5)	\int\:x\ln(x+5)dx
(\partial)/(\partial x)(ln(x^2+y^5))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y^{5}))
integral of ln(sqrt(x+2))	\int\:\ln(\sqrt{x+2})dx
integral of 7x^3e^x	\int\:7x^{3}e^{x}dx
tangent of f(x)=x^2-3x+4,\at x=1	tangent\:f(x)=x^{2}-3x+4,\at\:x=1
(dy)/(dt)+2ty=2te^{-t^2}	\frac{dy}{dt}+2ty=2te^{-t^{2}}
(\partial)/(\partial z)(xycos(z))	\frac{\partial\:}{\partial\:z}(xy\cos(z))
integral of x^6-4x^4+x+1	\int\:x^{6}-4x^{4}+x+1dx
integral of (t^5)/(sqrt(t^2+10))	\int\:\frac{t^{5}}{\sqrt{t^{2}+10}}dt
(dy)/(dx)=0.5(100-y)	\frac{dy}{dx}=0.5(100-y)
integral from 1 to 5 of sqrt(x)ln(x)	\int\:_{1}^{5}\sqrt{x}\ln(x)dx
derivative of f(x)=x(x+3)^2	derivative\:f(x)=x(x+3)^{2}
integral from 4 to infinity of 1/(x^3)	\int\:_{4}^{\infty\:}\frac{1}{x^{3}}dx
y^'-2y=7	y^{\prime\:}-2y=7
(\partial)/(\partial x)(x+yz)	\frac{\partial\:}{\partial\:x}(x+yz)
derivative of 6+x	\frac{d}{dx}(6+x)
limit as x approaches 0 of (8/(1+x)-8)/x	\lim\:_{x\to\:0}(\frac{\frac{8}{1+x}-8}{x})
integral of (1-(x+2)cot(x))/(sin(x))	\int\:\frac{1-(x+2)\cot(x)}{\sin(x)}dx
derivative of log_{6}(x^2-5x)	derivative\:\log_{6}(x^{2}-5x)
integral from 0 to pi/3 of 7sec^2(x)	\int\:_{0}^{\frac{π}{3}}7\sec^{2}(x)dx
derivative of cos(x*sin(y))	\frac{d}{dx}(\cos(x)\cdot\:\sin(y))
(\partial)/(\partial x)(3ln(x))	\frac{\partial\:}{\partial\:x}(3\ln(x))
area (sqrt(x+6)),x,-2,3	area\:(\sqrt{x+6}),x,-2,3
integral of sec^6(x)tan(x)	\int\:\sec^{6}(x)\tan(x)dx
derivative of y=23^x	derivative\:y=23^{x}
derivative of y=sqrt(ln(7x))	derivative\:y=\sqrt{\ln(7x)}
derivative of e^{x^3+3x}	\frac{d}{dx}(e^{x^{3}+3x})
limit as x approaches 2 of (\|x-2\|)/2	\lim\:_{x\to\:2}(\frac{\left\|x-2\right\|}{2})
slope of 10(1.05)^x	slope\:10(1.05)^{x}
integral from 0 to pi of cos(t)sin(t)	\int\:_{0}^{π}\cos(t)\sin(t)dt
sum from n=0 to infinity of (x^n)/n	\sum\:_{n=0}^{\infty\:}\frac{x^{n}}{n}
derivative of 3,x	\frac{d}{dx}(3,x)
limit as x approaches+0 of (sqrt(x))/x	\lim\:_{x\to\:+0}(\frac{\sqrt{x}}{x})
derivative of (x^3-3xln(2x+1))	\frac{d}{dx}((x^{3}-3x)\ln(2x+1))
y^{''}-2y^'+10y=x^2*e^x	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=x^{2}\cdot\:e^{x}
tangent of f(x)=(5x-x^2)(5-x-x^2),\at x=1	tangent\:f(x)=(5x-x^{2})(5-x-x^{2}),\at\:x=1
tangent of f(x)=sqrt(x-3)	tangent\:f(x)=\sqrt{x-3}
integral from-4 to 2 of f(x)+2x+5	\int\:_{-4}^{2}f(x)+2x+5dx
laplacetransform 1/2 cos(2t)	laplacetransform\:\frac{1}{2}\cos(2t)
integral of 1/(usqrt(a^2-u^2))	\int\:\frac{1}{u\sqrt{a^{2}-u^{2}}}du
(\partial)/(\partial z)(cos(xyz))	\frac{\partial\:}{\partial\:z}(\cos(xyz))
(dy)/(dt)=1.4y	\frac{dy}{dt}=1.4y
integral of 1/(-x^2-1)	\int\:\frac{1}{-x^{2}-1}dx
derivative of y=\sqrt[3]{t}(t^2+4)	derivative\:y=\sqrt[3]{t}(t^{2}+4)
y^'=((xy^3))/(25)	y^{\prime\:}=\frac{(xy^{3})}{25}
(dy)/(dx)=(6y)/(x^2)	\frac{dy}{dx}=\frac{6y}{x^{2}}
integral of-18t+4	\int\:-18t+4dt
integral of csc^2(x)+5	\int\:\csc^{2}(x)+5dx
(sqrt(1-x))^'	(\sqrt{1-x})^{\prime\:}
(\partial)/(\partial x)(-2xe^{-x^2})	\frac{\partial\:}{\partial\:x}(-2xe^{-x^{2}})
16y^{''}-40y^'+25y=0	16y^{\prime\:\prime\:}-40y^{\prime\:}+25y=0
derivative of sec^2(x)	derivative\:\sec^{2}(x)
2y^{''}+17y^'-9y=0	2y^{\prime\:\prime\:}+17y^{\prime\:}-9y=0
d/(d{y)}({x}{y}+{y}{z}+{x}{z})	\frac{d}{d{y}}({x}{y}+{y}{z}+{x}{z})
y^'=3e^{x-y}	y^{\prime\:}=3e^{x-y}
f(x)=tan(4x)	f(x)=\tan(4x)
(dy)/(dt)=3+5y	\frac{dy}{dt}=3+5y
derivative of 8^{sqrt(2s-1)}	derivative\:8^{\sqrt{2s-1}}
area y=-x^2+4,y=3x^2	area\:y=-x^{2}+4,y=3x^{2}
derivative of log_{2}(2x+4)	\frac{d}{dx}(\log_{2}(2x+4))
integral of x^7sqrt(ax^8-b)	\int\:x^{7}\sqrt{ax^{8}-b}dx
derivative of (2x/(x^2+2))	\frac{d}{dx}(\frac{2x}{x^{2}+2})
derivative of tan^2(sqrt(x))	\frac{d}{dx}(\tan^{2}(\sqrt{x}))
limit as x approaches 0 of e^{4x+2}	\lim\:_{x\to\:0}(e^{4x+2})
derivative of f(x)=(1+tan(2x))^3	derivative\:f(x)=(1+\tan(2x))^{3}
derivative of sin(-5x)	derivative\:\sin(-5x)
integral of 1/(cos(u)+1)	\int\:\frac{1}{\cos(u)+1}du
(dy)/(dx)=6xsqrt(8y+17)	\frac{dy}{dx}=6x\sqrt{8y+17}
(dy)/(dx)=x^2+y/x	\frac{dy}{dx}=x^{2}+\frac{y}{x}
integral of (-1)/(1+sin(x))	\int\:\frac{-1}{1+\sin(x)}dx
derivative of f(x)=sin(x)*cos(x)	derivative\:f(x)=\sin(x)\cdot\:\cos(x)
inverse oflaplace 3/(s^2+4)	inverselaplace\:\frac{3}{s^{2}+4}
laplacetransform cos(t-pi)	laplacetransform\:\cos(t-π)
area-2x^2+8,3x+1,x=0	area\:-2x^{2}+8,3x+1,x=0
7y^{''}+21y^'-28y=0	7y^{\prime\:\prime\:}+21y^{\prime\:}-28y=0
limit as x approaches 0 of (x^3+1)/(x^5)	\lim\:_{x\to\:0}(\frac{x^{3}+1}{x^{5}})
laplacetransform cos(6t)	laplacetransform\:\cos(6t)
derivative of 1/((x^2+1^{3/2)})	\frac{d}{dx}(\frac{1}{(x^{2}+1)^{\frac{3}{2}}})
f(x)=(1-5x)/(x+3)	f(x)=\frac{1-5x}{x+3}
derivative of x^{8/x}	\frac{d}{dx}(x^{\frac{8}{x}})
limit as x approaches pi of ln(cos(x)-8)	\lim\:_{x\to\:π}(\ln(\cos(x)-8))
laplacetransform cos(5t)	laplacetransform\:\cos(5t)
limit as x approaches 2 of x/((-x+2)^2)	\lim\:_{x\to\:2}(\frac{x}{(-x+2)^{2}})
(dy)/(dx)=(y^2+5xsqrt(x^2+y^2))/(xy)	\frac{dy}{dx}=\frac{y^{2}+5x\sqrt{x^{2}+y^{2}}}{xy}
9y^{''}-18y^'+11y=0	9y^{\prime\:\prime\:}-18y^{\prime\:}+11y=0
limit as x approaches-4 of (2x+3)/(x+4)	\lim\:_{x\to\:-4}(\frac{2x+3}{x+4})
derivative of (a-xsqrt(a+x))	\frac{d}{dx}((a-x)\sqrt{a+x})
derivative of e^{2x}cos(pix)	\frac{d}{dx}(e^{2x}\cos(πx))
integral of sin(ln(8x))	\int\:\sin(\ln(8x))dx
derivative of arcsin(x)	derivative\:\arcsin(x)

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