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

The derivative of (e^x/(sqrt(1-e^{2x))}) is (e^x)/((1-e^{2x))sqrt(1-e^{2x)}}

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

The first derivative of (e^x/(sqrt(1-e^{2x))}) is (e^x)/((1-e^{2x))sqrt(1-e^{2x)}}

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{56}{1 - cos ( 8 x )} d x

(- 1, 2), (4, 3)

\frac{d ^{4}}{d x ^{4}} (16 e^{x^{2}})

\frac{d}{d x} (\frac{8 x + 3}{0.2 x ^{2} + 1})

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

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