What is the derivative of (4x^2-13^{-11}) ?

The derivative of (4x^2-13^{-11}) is -(88x)/((4x^2-13)^{12)}

What is the first derivative of (4x^2-13^{-11}) ?

The first derivative of (4x^2-13^{-11}) is -(88x)/((4x^2-13)^{12)}

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\frac{d}{d x} ((4 x^{2} - 13)^{- 11})

- \frac{88 x}{( 4 x ^{2} - 13 ) ^{12}}

Solution steps

\frac{d}{d x} ((4 x^{2} - 13)^{- 11})

Apply the chain rule:

- \frac{11}{( 4 x ^{2} - 13 ) ^{12}} \frac{d}{d x} (4 x^{2} - 13)

= - \frac{11}{( 4 x ^{2} - 13 ) ^{12}} \frac{d}{d x} (4 x^{2} - 13)

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

= - \frac{11}{( 4 x ^{2} - 13 ) ^{12}} \cdot 8 x

Simplify

- \frac{11}{( 4 x ^{2} - 13 ) ^{12}} \cdot 8 x : - \frac{88 x}{( 4 x ^{2} - 13 ) ^{12}}

= - \frac{88 x}{( 4 x ^{2} - 13 ) ^{12}}

What is the derivative of (4x^2-13^{-11}) ?
The derivative of (4x^2-13^{-11}) is -(88x)/((4x^2-13)^{12)}
What is the first derivative of (4x^2-13^{-11}) ?
The first derivative of (4x^2-13^{-11}) is -(88x)/((4x^2-13)^{12)}