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)

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derivative of

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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}}

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)