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

The derivative of arcsec(x^3) is 3/(xsqrt(x^6-1))

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

The first derivative of arcsec(x^3) is 3/(xsqrt(x^6-1))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of arcsec(x^3) ?
The derivative of arcsec(x^3) is 3/(xsqrt(x^6-1))
What is the first derivative of arcsec(x^3) ?
The first derivative of arcsec(x^3) is 3/(xsqrt(x^6-1))