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Popular Calculus >

derivative of xarcsec(x^3)

Solution

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

Solution

arcsec (x^{3}) + \frac{3}{x ^{6} - 1}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = arcsec (x^{3})

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

\frac{d x}{d x} = 1

\frac{d}{d x} (arcsec (x^{3})) = \frac{3}{x x ^{6} - 1}

= 1 \cdot arcsec (x^{3}) + \frac{3}{x x ^{6} - 1} x

Simplify

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

= arcsec (x^{3}) + \frac{3}{x ^{6} - 1}

Graph

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Frequently Asked Questions (FAQ)

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