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Popular >

derivative of (4x^2-14^{-10})

Solution

\frac{d}{d x} ((4 x^{2} - 14)^{- 10})

Solution

- \frac{5 x}{128 ( 2 x ^{2} - 7 ) ^{11}}

Solution steps

\frac{d}{d x} ((4 x^{2} - 14)^{- 10})

Apply the chain rule:

- \frac{10}{( 4 x ^{2} - 14 ) ^{11}} \frac{d}{d x} (4 x^{2} - 14)

= - \frac{10}{( 4 x ^{2} - 14 ) ^{11}} \frac{d}{d x} (4 x^{2} - 14)

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

= - \frac{10}{( 4 x ^{2} - 14 ) ^{11}} \cdot 8 x

Simplify

- \frac{10}{( 4 x ^{2} - 14 ) ^{11}} \cdot 8 x : - \frac{5 x}{128 ( 2 x ^{2} - 7 ) ^{11}}

= - \frac{5 x}{128 ( 2 x ^{2} - 7 ) ^{11}}

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Frequently Asked Questions (FAQ)

What is the derivative of (4x^2-14^{-10}) ?
The derivative of (4x^2-14^{-10}) is -(5x)/(128(2x^2-7)^{11)}
What is the first derivative of (4x^2-14^{-10}) ?
The first derivative of (4x^2-14^{-10}) is -(5x)/(128(2x^2-7)^{11)}