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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Graph

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\int 2 x y + y^{2}

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\int \frac{sec ( x ) + cos ( x )}{9 cos ( x )} d x

Frequently Asked Questions (FAQ)

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