What is the derivative of x/(3+e^x) ?

The derivative of x/(3+e^x) is (3+e^x-e^xx)/((3+e^x)^2)

What is the first derivative of x/(3+e^x) ?

The first derivative of x/(3+e^x) is (3+e^x-e^xx)/((3+e^x)^2)

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\frac{d}{d x} (\frac{x}{3 + e ^{x}})

\frac{3 + e ^{x} - e ^{x} x}{( 3 + e ^{x} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{3 + e ^{x}})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 3 + e ^{x} ) - \frac{d}{d x} ( 3 + e ^{x} ) x}{( 3 + e ^{x} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (3 + e^{x}) = e^{x}

= \frac{1 \cdot ( 3 + e ^{x} ) - e ^{x} x}{( 3 + e ^{x} ) ^{2}}

Simplify

= \frac{3 + e ^{x} - e ^{x} x}{( 3 + e ^{x} ) ^{2}}

What is the derivative of x/(3+e^x) ?
The derivative of x/(3+e^x) is (3+e^x-e^xx)/((3+e^x)^2)
What is the first derivative of x/(3+e^x) ?
The first derivative of x/(3+e^x) is (3+e^x-e^xx)/((3+e^x)^2)