What is the derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} ?

The derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} is -(4e^{2x}(-e^{2x}-1))/((e^{2x)-1)^3}

What is the first derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} ?

The first derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} is -(4e^{2x}(-e^{2x}-1))/((e^{2x)-1)^3}

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derivative of

f (x) = - \frac{2 e ^{2 x}}{( e ^{2 x} - 1 ) ^{2}}

- \frac{4 e ^{2 x} ( - e ^{2 x} - 1 )}{( e ^{2 x} - 1 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} ((e^{2 x} - 1)^{2}) = 4 e^{2 x} (e^{2 x} - 1)

= - 2 \cdot \frac{e ^{2 x} \cdot 2 ( e ^{2 x} - 1 ) ^{2} - 4 e ^{2 x} ( e ^{2 x} - 1 ) e ^{2 x}}{( ( e ^{2 x} - 1 ) ^{2} ) ^{2}}

Simplify

- 2 \cdot \frac{e ^{2 x} \cdot 2 ( e ^{2 x} - 1 ) ^{2} - 4 e ^{2 x} ( e ^{2 x} - 1 ) e ^{2 x}}{( ( e ^{2 x} - 1 ) ^{2} ) ^{2}} : - \frac{4 e ^{2 x} ( - e ^{2 x} - 1 )}{( e ^{2 x} - 1 ) ^{3}}

= - \frac{4 e ^{2 x} ( - e ^{2 x} - 1 )}{( e ^{2 x} - 1 ) ^{3}}

What is the derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} ?
The derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} is -(4e^{2x}(-e^{2x}-1))/((e^{2x)-1)^3}
What is the first derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} ?
The first derivative of f(x)=-(2e^{2x})/((e^{2x)-1)^2} is -(4e^{2x}(-e^{2x}-1))/((e^{2x)-1)^3}