What is the derivative of (3x^2-10)^{-13} ?

The derivative of (3x^2-10)^{-13} is -(78x)/((3x^2-10)^{14)}

What is the first derivative of (3x^2-10)^{-13} ?

The first derivative of (3x^2-10)^{-13} is -(78x)/((3x^2-10)^{14)}

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derivative of

(3 x^{2} - 10)^{- 13}

- \frac{78 x}{( 3 x ^{2} - 10 ) ^{14}}

Solution steps

\frac{d}{d x} ((3 x^{2} - 10)^{- 13})

Apply the chain rule:

- \frac{13}{( 3 x ^{2} - 10 ) ^{14}} \frac{d}{d x} (3 x^{2} - 10)

= - \frac{13}{( 3 x ^{2} - 10 ) ^{14}} \frac{d}{d x} (3 x^{2} - 10)

\frac{d}{d x} (3 x^{2} - 10) = 6 x

= - \frac{13}{( 3 x ^{2} - 10 ) ^{14}} \cdot 6 x

Simplify

- \frac{13}{( 3 x ^{2} - 10 ) ^{14}} \cdot 6 x : - \frac{78 x}{( 3 x ^{2} - 10 ) ^{14}}

= - \frac{78 x}{( 3 x ^{2} - 10 ) ^{14}}

What is the derivative of (3x^2-10)^{-13} ?
The derivative of (3x^2-10)^{-13} is -(78x)/((3x^2-10)^{14)}
What is the first derivative of (3x^2-10)^{-13} ?
The first derivative of (3x^2-10)^{-13} is -(78x)/((3x^2-10)^{14)}