Find the derivative of . x^ -4 (3-4x^ -5 ) - Vidyadip

Question

Find the derivative of . $\text{x}^{-4}(3-4\text{x}^{-5})$

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Answer

Let $\text{f}(\text{x})=\text{x}^{-4}(3-4\text{x}^{-5})$ By Leibnitz product rule, $\text{f}'\big(\text{x})=\text{x}^{-4}\frac{\text{d}}{\text{dx}}\big(3-4\text{x}^{-5}\big)+\big(3-4\text{x}^{-5}\big)\frac{\text{d}}{\text{dx}}\big(\text{x}^{-4}\big)$ $=\text{x}^{-4}\big\{0-4(-5)\text{x}^{-5-1}\big\}+(3-4\text{x}^{-5})(-4)(\text{x}^{-4-1})$ $=\text{x}^{-4}(20\text{x}^{-6})+(3-4\text{x}^{-5})(-4\text{x}^{-5})$ $=20\text{x}^{-10}-12\text{x}^{-5}+16\text{x}^{-10}$ $=36\text{x}^{-10}-12\text{x}^{-5}$ $=-\frac{12}{\text{x}^5}+\frac{36}{\text{x}^{10}}$

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