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Popular >

derivative of (2x^2-5^{-12})

Solution

\frac{d}{d x} ((2 x^{2} - 5)^{- 12})

Solution

- \frac{48 x}{( 2 x ^{2} - 5 ) ^{13}}

Solution steps

\frac{d}{d x} ((2 x^{2} - 5)^{- 12})

Apply the chain rule:

- \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \frac{d}{d x} (2 x^{2} - 5)

= - \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \frac{d}{d x} (2 x^{2} - 5)

\frac{d}{d x} (2 x^{2} - 5) = 4 x

= - \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \cdot 4 x

Simplify

- \frac{12}{( 2 x ^{2} - 5 ) ^{13}} \cdot 4 x : - \frac{48 x}{( 2 x ^{2} - 5 ) ^{13}}

= - \frac{48 x}{( 2 x ^{2} - 5 ) ^{13}}

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Frequently Asked Questions (FAQ)

What is the derivative of (2x^2-5^{-12}) ?
The derivative of (2x^2-5^{-12}) is -(48x)/((2x^2-5)^{13)}
What is the first derivative of (2x^2-5^{-12}) ?
The first derivative of (2x^2-5^{-12}) is -(48x)/((2x^2-5)^{13)}