Derivatives of Powers of linear expressions

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Find the derivative $\;\;\;\frac{d}{dx}\left(19x^{\frac{-2}{7}}-8x^{\frac{-7}{4}}\right)^{-3}$

**Answer**

$\;\;\;\frac{d}{dx}\left(19x^{\frac{-2}{7}}-8x^{\frac{-7}{4}}\right)^{-3}$

$=-3\left(19x^{\frac{-2}{7}}-8x^{\frac{-7}{4}}\right)^{-4}\left(-\frac{38}{7}x^{\frac{-9}{7}}+14x^{\frac{-11}{4}}\right)$