Differentiate the following function with respect to x:x^ -4 (3-4… - Vidyadip

Question

Differentiate the following function with respect to x:$\text{x}^{-4}(3-\text{4x}^{-5})$

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Answer

Let $\text{u}=\text{x}^{-4};\text{v}=(3-\text{4x}^{-5})$Then, $\text{u}'=-\text{4x}^{-5};\text{v}'=\text{20x}^{-6}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[\text{x}^{-4}(3-\text{4x}^{-5})]=\text{x}^{-4}(\text{20x}^{-6})+(3-\text{4x}^{-5})(-\text{4x}^{-5})$
$=\text{20x}^{-10}-\text{12x}^{-5}+\text{16x}^{-10}$
$=-\text{12x}^{-5}+\text{36x}^{-10}$

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