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Popular >

derivative of (3x^2-9^{-13})

Solution

\frac{d}{d x} ((3 x^{2} - 9)^{- 13})

Solution

- \frac{26 x}{1594323 ( x ^{2} - 3 ) ^{14}}

Solution steps

\frac{d}{d x} ((3 x^{2} - 9)^{- 13})

Apply the chain rule:

- \frac{13}{( 3 x ^{2} - 9 ) ^{14}} \frac{d}{d x} (3 x^{2} - 9)

= - \frac{13}{( 3 x ^{2} - 9 ) ^{14}} \frac{d}{d x} (3 x^{2} - 9)

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

= - \frac{13}{( 3 x ^{2} - 9 ) ^{14}} \cdot 6 x

Simplify

- \frac{13}{( 3 x ^{2} - 9 ) ^{14}} \cdot 6 x : - \frac{26 x}{1594323 ( x ^{2} - 3 ) ^{14}}

= - \frac{26 x}{1594323 ( x ^{2} - 3 ) ^{14}}

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^2-9^{-13}) ?
The derivative of (3x^2-9^{-13}) is -(26x)/(1594323(x^2-3)^{14)}
What is the first derivative of (3x^2-9^{-13}) ?
The first derivative of (3x^2-9^{-13}) is -(26x)/(1594323(x^2-3)^{14)}