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

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

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

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

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derivative of

\frac{e ^{x}}{3 + e ^{x}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (9 x^{5} cos (x))

\frac{d}{d x} (x + x^{5})

ma c l a u r in \frac{1}{1 + x ^{4}}

a re a y = e^{x}, y = x, x = 0, x = 1

\int \frac{e ^{2 x}}{1 - e ^{4 x}} d x

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