What is the derivative of y=(e^{8x})/(e^{8x)+1} ?

The derivative of y=(e^{8x})/(e^{8x)+1} is (8e^{8x})/((e^{8x)+1)^2}

What is the first derivative of y=(e^{8x})/(e^{8x)+1} ?

The first derivative of y=(e^{8x})/(e^{8x)+1} is (8e^{8x})/((e^{8x)+1)^2}

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derivative of

y = \frac{e ^{8 x}}{e ^{8 x} + 1}

\frac{8 e ^{8 x}}{( e ^{8 x} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{8 x}}{e ^{8 x} + 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{8 x} ) ( e ^{8 x} + 1 ) - \frac{d}{d x} ( e ^{8 x} + 1 ) e ^{8 x}}{( e ^{8 x} + 1 ) ^{2}}

\frac{d}{d x} (e^{8 x}) = e^{8 x} \cdot 8

\frac{d}{d x} (e^{8 x} + 1) = 8 e^{8 x}

= \frac{e ^{8 x} \cdot 8 ( e ^{8 x} + 1 ) - 8 e ^{8 x} e ^{8 x}}{( e ^{8 x} + 1 ) ^{2}}

Simplify

\frac{e ^{8 x} \cdot 8 ( e ^{8 x} + 1 ) - 8 e ^{8 x} e ^{8 x}}{( e ^{8 x} + 1 ) ^{2}} : \frac{8 e ^{8 x}}{( e ^{8 x} + 1 ) ^{2}}

= \frac{8 e ^{8 x}}{( e ^{8 x} + 1 ) ^{2}}

\frac{50}{100 + 0.01 s}

x \to 0 lim (\frac{1}{( x + 1 ) ^{2}})

(e^{x^{2} + 1})^{^{'}}

x^{3} os (x)

11 sin (t) + 14 cos (t)

What is the derivative of y=(e^{8x})/(e^{8x)+1} ?
The derivative of y=(e^{8x})/(e^{8x)+1} is (8e^{8x})/((e^{8x)+1)^2}
What is the first derivative of y=(e^{8x})/(e^{8x)+1} ?
The first derivative of y=(e^{8x})/(e^{8x)+1} is (8e^{8x})/((e^{8x)+1)^2}