What is the derivative of (4x^2-13)^{-13} ?

The derivative of (4x^2-13)^{-13} is -(104x)/((4x^2-13)^{14)}

What is the first derivative of (4x^2-13)^{-13} ?

The first derivative of (4x^2-13)^{-13} is -(104x)/((4x^2-13)^{14)}

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derivative of

(4 x^{2} - 13)^{- 13}

- \frac{104 x}{( 4 x ^{2} - 13 ) ^{14}}

Solution steps

\frac{d}{d x} ((4 x^{2} - 13)^{- 13})

Apply the chain rule:

- \frac{13}{( 4 x ^{2} - 13 ) ^{14}} \frac{d}{d x} (4 x^{2} - 13)

= - \frac{13}{( 4 x ^{2} - 13 ) ^{14}} \frac{d}{d x} (4 x^{2} - 13)

\frac{d}{d x} (4 x^{2} - 13) = 8 x

= - \frac{13}{( 4 x ^{2} - 13 ) ^{14}} \cdot 8 x

Simplify

- \frac{13}{( 4 x ^{2} - 13 ) ^{14}} \cdot 8 x : - \frac{104 x}{( 4 x ^{2} - 13 ) ^{14}}

= - \frac{104 x}{( 4 x ^{2} - 13 ) ^{14}}

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What is the derivative of (4x^2-13)^{-13} ?
The derivative of (4x^2-13)^{-13} is -(104x)/((4x^2-13)^{14)}
What is the first derivative of (4x^2-13)^{-13} ?
The first derivative of (4x^2-13)^{-13} is -(104x)/((4x^2-13)^{14)}