What is the derivative of f(x)=(9-x^3)^{-2} ?

The derivative of f(x)=(9-x^3)^{-2} is (6x^2)/((9-x^3)^3)

What is the first derivative of f(x)=(9-x^3)^{-2} ?

The first derivative of f(x)=(9-x^3)^{-2} is (6x^2)/((9-x^3)^3)

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derivative of

f (x) = (9 - x^{3})^{- 2}

\frac{6 x ^{2}}{( 9 - x ^{3} ) ^{3}}

Solution steps

\frac{d}{d x} ((9 - x^{3})^{- 2})

Apply the chain rule:

- \frac{2}{( 9 - x ^{3} ) ^{3}} \frac{d}{d x} (9 - x^{3})

= - \frac{2}{( 9 - x ^{3} ) ^{3}} \frac{d}{d x} (9 - x^{3})

\frac{d}{d x} (9 - x^{3}) = - 3 x^{2}

= - \frac{2}{( 9 - x ^{3} ) ^{3}} (- 3 x^{2})

Simplify

- \frac{2}{( 9 - x ^{3} ) ^{3}} (- 3 x^{2}) : \frac{6 x ^{2}}{( 9 - x ^{3} ) ^{3}}

= \frac{6 x ^{2}}{( 9 - x ^{3} ) ^{3}}

What is the derivative of f(x)=(9-x^3)^{-2} ?
The derivative of f(x)=(9-x^3)^{-2} is (6x^2)/((9-x^3)^3)
What is the first derivative of f(x)=(9-x^3)^{-2} ?
The first derivative of f(x)=(9-x^3)^{-2} is (6x^2)/((9-x^3)^3)