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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
The differential coefficient of $\text{f}(\log\text{x}) \ w.r.t. x,$ where $\text{f(x)}=\log\text{x}$ is:
  • A
    $\frac{\text{x}}{\log\text{x}}$
  • B
    $\frac{\log\text{x}}{\text{x}}$
  • ✓
    $(\text{x}\log\text{x})^{-1}$
  • D
    None of these.
✓

Answer

Correct option: C.
$(\text{x}\log\text{x})^{-1}$
$\text{f(x)}=\log\text{x}$
$\Rightarrow\text{f}(\log\text{x})=\log(\log\text{x})$
$\Rightarrow\text{f}\ '(\log\text{x})=\frac{1}{\text{x}\log\text{x}}=(\text{x}\log\text{x})^{-1}$

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