What is the derivative of (arccos(x)^{10}) ?

The derivative of (arccos(x)^{10}) is -(10arccos^9(x))/(sqrt(1-x^2))

What is the first derivative of (arccos(x)^{10}) ?

The first derivative of (arccos(x)^{10}) is -(10arccos^9(x))/(sqrt(1-x^2))

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\frac{d}{d x} ((arccos (x))^{10})

- \frac{10 arccos ^{9} ( x )}{1 - x ^{2}}

Solution steps

\frac{d}{d x} ((arccos (x))^{10})

Apply the chain rule:

10 (arccos (x))^{9} \frac{d}{d x} (arccos (x))

= 10 (arccos (x))^{9} \frac{d}{d x} (arccos (x))

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

= 10 (arccos (x))^{9} (- \frac{1}{1 - x ^{2}})

Simplify

10 arccos^{9} (x) (- \frac{1}{1 - x ^{2}}) : - \frac{10 arccos ^{9} ( x )}{1 - x ^{2}}

= - \frac{10 arccos ^{9} ( x )}{1 - x ^{2}}

What is the derivative of (arccos(x)^{10}) ?
The derivative of (arccos(x)^{10}) is -(10arccos^9(x))/(sqrt(1-x^2))
What is the first derivative of (arccos(x)^{10}) ?
The first derivative of (arccos(x)^{10}) is -(10arccos^9(x))/(sqrt(1-x^2))