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Popular >

derivative of (e^x/(1+x^2))

Solution

\frac{d}{d x} (\frac{e ^{x}}{1 + x ^{2}})

Solution

\frac{e ^{x} ( 1 + x ^{2} ) - 2 x e ^{x}}{( 1 + x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{1 + x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{x} ) ( 1 + x ^{2} ) - \frac{d}{d x} ( 1 + x ^{2} ) e ^{x}}{( 1 + x ^{2} ) ^{2}}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (1 + x^{2}) = 2 x

= \frac{e ^{x} ( 1 + x ^{2} ) - 2 x e ^{x}}{( 1 + x ^{2} ) ^{2}}

Popular Examples

integral from 1 to 6 of 2/(x^3)

\int_{1}^{6} \frac{2}{x ^{3}} d x

tangent of 6-4x^2 tangent of

6 - 4 x^{2}

(dy)/(dx)-2/3 xy= 1/3 y^3

\frac{d y}{d x} - \frac{2}{3} x y = \frac{1}{3} y^{3}

integral of 4x^4(27+x^5)^{1/3}

\int 4 x^{4} (27 + x^{5})^{\frac{1}{3}} d x

integral of tsin(x)

\int t sin (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of (e^x/(1+x^2)) ?
The derivative of (e^x/(1+x^2)) is (e^x(1+x^2)-2xe^x)/((1+x^2)^2)
What is the first derivative of (e^x/(1+x^2)) ?
The first derivative of (e^x/(1+x^2)) is (e^x(1+x^2)-2xe^x)/((1+x^2)^2)