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

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

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

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

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derivative of

arcsec (e^{2 x})

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = 14 x^{8}

\frac{d}{d x} (x \cdot ∣ x ∣)

x \to - 1 lim (x + a)

x \to 2 lim (2 e^{x - 2})

\int \frac{4}{3} x d x

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