What is the derivative of arcsec(e^{3x}) ?

The derivative of arcsec(e^{3x}) is 3/(sqrt(e^{6x)-1)}

What is the first derivative of arcsec(e^{3x}) ?

The first derivative of arcsec(e^{3x}) is 3/(sqrt(e^{6x)-1)}

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\frac{d}{d x} (arcsec (e^{3 x}))

\frac{3}{e ^{6 x} - 1}

Solution steps

\frac{d}{d x} (arcsec (e^{3 x}))

Apply the chain rule:

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

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

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

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

Simplify

\frac{1}{( e ^{3 x} ) ^{2} ( e ^{3 x} ) ^{2} - 1} e^{3 x} \cdot 3 : \frac{3}{e ^{6 x} - 1}

= \frac{3}{e ^{6 x} - 1}

What is the derivative of arcsec(e^{3x}) ?
The derivative of arcsec(e^{3x}) is 3/(sqrt(e^{6x)-1)}
What is the first derivative of arcsec(e^{3x}) ?
The first derivative of arcsec(e^{3x}) is 3/(sqrt(e^{6x)-1)}