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))

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

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}

x y d x + (x + 1) d y = 0

\int (x^{2} - 4)^{3} (2 x) d x

f (x) = 7 x - 4 x, at x = 1

g (x) = 9 x e^{5 x}

\int - 5 x^{3} + \frac{3}{4} x^{2} d x

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))