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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Graph

Popular Examples

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(\partial)/(\partial y)(e^{x^2y})

\frac{\partial}{\partial y} (e^{x^{2} y})

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\int \frac{( 4 x - 11 )}{( x ^{3} - 9 x ^{2} )} d x

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\frac{d}{d x} (cos (wt) + sin (wt))

Frequently Asked Questions (FAQ)

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