What is the derivative of sqrt(9-x^8) ?

The derivative of sqrt(9-x^8) is -(4x^7)/(sqrt(9-x^8))

What is the first derivative of sqrt(9-x^8) ?

The first derivative of sqrt(9-x^8) is -(4x^7)/(sqrt(9-x^8))

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\frac{d}{d x} (9 - x^{8})

- \frac{4 x ^{7}}{9 - x ^{8}}

Solution steps

\frac{d}{d x} (9 - x^{8})

Apply the chain rule:

\frac{1}{2 9 - x ^{8}} \frac{d}{d x} (9 - x^{8})

= \frac{1}{2 9 - x ^{8}} \frac{d}{d x} (9 - x^{8})

\frac{d}{d x} (9 - x^{8}) = - 8 x^{7}

= \frac{1}{2 9 - x ^{8}} (- 8 x^{7})

Simplify

\frac{1}{2 9 - x ^{8}} (- 8 x^{7}) : - \frac{4 x ^{7}}{9 - x ^{8}}

= - \frac{4 x ^{7}}{9 - x ^{8}}

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What is the derivative of sqrt(9-x^8) ?
The derivative of sqrt(9-x^8) is -(4x^7)/(sqrt(9-x^8))
What is the first derivative of sqrt(9-x^8) ?
The first derivative of sqrt(9-x^8) is -(4x^7)/(sqrt(9-x^8))