What is the derivative of arcsec(x^8) ?

The derivative of arcsec(x^8) is (8x^7)/(sqrt(x^{16))sqrt(x^{16)-1}}

What is the first derivative of arcsec(x^8) ?

The first derivative of arcsec(x^8) is (8x^7)/(sqrt(x^{16))sqrt(x^{16)-1}}

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derivative of

arcsec (x^{8})

\frac{8 x ^{7}}{x ^{16} x ^{16} - 1}

Solution steps

\frac{d}{d x} (arcsec (x^{8}))

Apply the chain rule:

\frac{1}{( x ^{8} ) ^{2} ( x ^{8} ) ^{2} - 1} \frac{d}{d x} (x^{8})

= \frac{1}{( x ^{8} ) ^{2} ( x ^{8} ) ^{2} - 1} \frac{d}{d x} (x^{8})

\frac{d}{d x} (x^{8}) = 8 x^{7}

= \frac{1}{( x ^{8} ) ^{2} ( x ^{8} ) ^{2} - 1} \cdot 8 x^{7}

Simplify

\frac{1}{( x ^{8} ) ^{2} ( x ^{8} ) ^{2} - 1} \cdot 8 x^{7} : \frac{8 x ^{7}}{x ^{16} x ^{16} - 1}

= \frac{8 x ^{7}}{x ^{16} x ^{16} - 1}

What is the derivative of arcsec(x^8) ?
The derivative of arcsec(x^8) is (8x^7)/(sqrt(x^{16))sqrt(x^{16)-1}}
What is the first derivative of arcsec(x^8) ?
The first derivative of arcsec(x^8) is (8x^7)/(sqrt(x^{16))sqrt(x^{16)-1}}