What is the derivative of f(x)=(arcsec(x))^{13} ?

The derivative of f(x)=(arcsec(x))^{13} is (13arcsec^{12}(x))/(sqrt(x^2)\sqrt{x^2-1)}

What is the first derivative of f(x)=(arcsec(x))^{13} ?

The first derivative of f(x)=(arcsec(x))^{13} is (13arcsec^{12}(x))/(sqrt(x^2)\sqrt{x^2-1)}

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derivative of

f (x) = (arcsec (x))^{13}

\frac{13 arcsec ^{12} ( x )}{x ^{2} x ^{2} - 1}

Solution steps

\frac{d}{d x} ((arcsec (x))^{13})

Apply the chain rule:

13 (arcsec (x))^{12} \frac{d}{d x} (arcsec (x))

= 13 (arcsec (x))^{12} \frac{d}{d x} (arcsec (x))

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

= 13 (arcsec (x))^{12} \frac{1}{x ^{2} x ^{2} - 1}

Simplify

13 arcsec^{12} (x) \frac{1}{x ^{2} x ^{2} - 1} : \frac{13 arcsec ^{12} ( x )}{x ^{2} x ^{2} - 1}

= \frac{13 arcsec ^{12} ( x )}{x ^{2} x ^{2} - 1}

\int 3 x sin^{2} (x) d x

\int_{0}^{1} - \frac{1}{x - 5} + \frac{2}{x - 2} d x

\frac{d}{d x} (ln (x^{- 2}))

\int (2 x + 6)^{5} d x

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What is the derivative of f(x)=(arcsec(x))^{13} ?
The derivative of f(x)=(arcsec(x))^{13} is (13arcsec^{12}(x))/(sqrt(x^2)\sqrt{x^2-1)}
What is the first derivative of f(x)=(arcsec(x))^{13} ?
The first derivative of f(x)=(arcsec(x))^{13} is (13arcsec^{12}(x))/(sqrt(x^2)\sqrt{x^2-1)}