What is the derivative of (e^x)/(1+x) ?

The derivative of (e^x)/(1+x) is (e^xx)/((1+x)^2)

What is the first derivative of (e^x)/(1+x) ?

The first derivative of (e^x)/(1+x) is (e^xx)/((1+x)^2)

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derivative of

\frac{e ^{x}}{1 + x}

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

Solution steps

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

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

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

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

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

Simplify

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

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

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