What is the derivative of arcsin(e^{2x}) ?

The derivative of arcsin(e^{2x}) is (2e^{2x})/(sqrt(1-e^{4x))}

What is the first derivative of arcsin(e^{2x}) ?

The first derivative of arcsin(e^{2x}) is (2e^{2x})/(sqrt(1-e^{4x))}

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\frac{d}{d x} (arcsin (e^{2 x}))

\frac{2 e ^{2 x}}{1 - e ^{4 x}}

Solution steps

\frac{d}{d x} (arcsin (e^{2 x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

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