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LIMITS AND DERIVATIVES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLIMITS AND DERIVATIVES2 Marks
Question
Find the derivative of. $\text{x}^{-3}(5+3\text{x})$
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Answer

Let $\text{f}(\text{x})=\text{x}^{-3}(5+3\text{x})$ By Leibnitz product rule, $\text{f}'\big(\text{x})=(\text{x}^{-3}\big)\frac{\text{d}}{\text{dx}}\big(5+3\text{x}\big)+\big(5+3\text{x}\big)\frac{\text{d}}{\text{dx}}\big(\text{x}^{-3}\big)$ $=\text{x}^{-3}(0+3)+(5+3\text{x})(-3\text{x}^{-3-1})$ $=\text{x}^{-3}(3)+(5+3\text{x})(-3\text{x}^{-4})$ $=3\text{x}^{-3}-15\text{x}^{-4}-9\text{x}^{-3}$ $=-6\text{x}^{-3}-15\text{x}^{-4}$ $=-3\text{x}^{-3}\Big(2+\frac{5}{\text{x}}\Big)$ $=\frac{-3\text{x}^{-3}}{\text{x}}\big(2{\text{x}+5}\big)$ $=\frac{-3}{\text{x}^4}\big(5+2{\text{x}}\big)$

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