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Popular >

derivative of (2-3x^3)^{-2}

Solution

derivative of

(2 - 3 x^{3})^{- 2}

Solution

\frac{18 x ^{2}}{( 2 - 3 x ^{3} ) ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{2}{( 2 - 3 x ^{3} ) ^{3}} (- 9 x^{2}) : \frac{18 x ^{2}}{( 2 - 3 x ^{3} ) ^{3}}

= \frac{18 x ^{2}}{( 2 - 3 x ^{3} ) ^{3}}

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Frequently Asked Questions (FAQ)

What is the derivative of (2-3x^3)^{-2} ?
The derivative of (2-3x^3)^{-2} is (18x^2)/((2-3x^3)^3)
What is the first derivative of (2-3x^3)^{-2} ?
The first derivative of (2-3x^3)^{-2} is (18x^2)/((2-3x^3)^3)