CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives3 Marks
Question
Differentiate the following functions with respect to x:$\frac{3^\text{x}}{\text{x}+\tan\text{x}}$
✓
Answer
We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{3^\text{x}}{\text{x}+\tan\text{x}}\Big)$
Using quotient rule, we get
$\frac{(\text{x}+\tan\text{x})\frac{\text{d}}{\text{dx}}(3^\text{x})-(3^\text{x})\frac{\text{d}}{\text{dx}}(\text{x}+\tan\text{x})}{(\text{x}+\tan\text{x})^2}$
$=\frac{(\text{x}+\tan\text{x})\times3^\text{x}\log3-3^\text{x}(1+\sec^2\text{x})}{(\text{x}+\tan\text{x})^2}$
$=\frac{3^\text{x}\Big\{(\text{x}+\tan\text{x})\log3-(1+\sec^2\text{x})\Big\}}{(\text{x}+\tan\text{x})^2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.