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

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

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

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

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derivative of

f (x) = \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}}

x \to 3 - lim (x^{2} - 9)

y = 3 (x + 1), y = 4 (x + 1), x = 6

\int \frac{- 341 x + 342}{x ^{2} + x - 2} d x

\frac{\partial}{\partial x} (3 x sin (9 x^{2} y))

x \to \infty lim ((1 + x)^{\frac{3}{x}})

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