What is the derivative of (7e^x)/((7+e^x)^2) ?

The derivative of (7e^x)/((7+e^x)^2) is (7e^x(-e^x+7))/((7+e^x)^3)

What is the first derivative of (7e^x)/((7+e^x)^2) ?

The first derivative of (7e^x)/((7+e^x)^2) is (7e^x(-e^x+7))/((7+e^x)^3)

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derivative of

\frac{7 e ^{x}}{( 7 + e ^{x} ) ^{2}}

\frac{7 e ^{x} ( - e ^{x} + 7 )}{( 7 + e ^{x} ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{7 e ^{x}}{( 7 + e ^{x} ) ^{2}})

Take the constant out:

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

= 7 \frac{d}{d x} (\frac{e ^{x}}{( 7 + e ^{x} ) ^{2}})

Apply the Quotient Rule:

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

= 7 \cdot \frac{\frac{d}{d x} ( e ^{x} ) ( 7 + e ^{x} ) ^{2} - \frac{d}{d x} ( ( 7 + e ^{x} ) ^{2} ) e ^{x}}{( ( 7 + e ^{x} ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((7 + e^{x})^{2}) = 2 (7 + e^{x}) e^{x}

= 7 \cdot \frac{e ^{x} ( 7 + e ^{x} ) ^{2} - 2 ( 7 + e ^{x} ) e ^{x} e ^{x}}{( ( 7 + e ^{x} ) ^{2} ) ^{2}}

Simplify

7 \cdot \frac{e ^{x} ( 7 + e ^{x} ) ^{2} - 2 ( 7 + e ^{x} ) e ^{x} e ^{x}}{( ( 7 + e ^{x} ) ^{2} ) ^{2}} : \frac{7 e ^{x} ( - e ^{x} + 7 )}{( 7 + e ^{x} ) ^{3}}

= \frac{7 e ^{x} ( - e ^{x} + 7 )}{( 7 + e ^{x} ) ^{3}}

\frac{d}{d t} (t^{r})

\int \frac{1}{x ^{2} + 10} d x

\int \frac{2}{- x ^{2} + 5} d x

\frac{s}{s ^{2} + 2 s + 4}

\int + ln (x) d x

What is the derivative of (7e^x)/((7+e^x)^2) ?
The derivative of (7e^x)/((7+e^x)^2) is (7e^x(-e^x+7))/((7+e^x)^3)
What is the first derivative of (7e^x)/((7+e^x)^2) ?
The first derivative of (7e^x)/((7+e^x)^2) is (7e^x(-e^x+7))/((7+e^x)^3)