Differentiate the following function with respect to x:x^5(3-6x^ … - Vidyadip

Question

Differentiate the following function with respect to x:$\text{x}^5(3-\text{6x}^{-9})$

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Answer

Let $\text{u}=\text{x}^5;\text{v}=(3-\text{6x}^{-9})$Then, $\text{u}'=\text{5x}^4;\text{v}'=\text{54x}^{-10}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[\text{x}^5(3-\text{6x}^9)]=\text{x}^5(\text{54x}^{-10})+\text{5x}^4(3-\text{6x}^9)$
$=\text{54x}^{-5}+\text{15x}^4-\text{30x}^{-5}$
$=\text{15x}^4+\text{24x}^{-5}$

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