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})

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}}

x \to 1 lim (∣ x - 1 ∣)

\frac{d}{d x} (\frac{x - 2}{x})

\frac{d}{d x} (\frac{3 x}{2 y})

\int x^{3} 1 + 9 x^{2} d x

\int 1 + 3 x^{2} d x

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)