CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives3 Marks
Question
Differentiate the following function with respect to x:$\text{x}^{-3}(5+\text{3x})$
✓
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:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}[\text{x}^{-3}(5+\text{3x})]=\text{x}^{-3}.3+(5+\text{3x})(-3\text{x}^{-4})$
$=\text{3x}^{-3}-\text{15x}^{-4}-\text{9x}^{-3}$
$=-\text{15x}^{-4}-\text{6x}^{-3}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.