Differentiate the following function with respect to x:x^ -3 (5+3… - Vidyadip

Question

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

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Answer

Let $\text{u}=\text{x}^{-3};\text{v}=(5+\text{3x})$Then, $\text{u}'=-\text{3x}^{-4};\text{v}'=3$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[\text{x}^{-3}(5+\text{3x})]=\text{x}^{-3}.3+(5+\text{3x})(-3\text{x}^{-4})$
$=\text{3x}^{-3}-\text{15x}^{-4}-\text{9x}^{-3}$
$=-\text{15x}^{-4}-\text{6x}^{-3}$

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