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Mathematics · 2025 · 3 marks
CBSE 2025 · Region 7 · Set 1 · Q28
Differentiate y =√(log { sin ((x^3)/3-1)}) with respect to x.
Differentiate $\displaystyle \mathrm{y}=\sqrt{\log \left\{\sin \left(\frac{\mathrm{x}^{3}}{3}-1\right)\right\}}$ with respect to x .
Marking-scheme solution
\[\begin{aligned}
\frac{d \mathrm{y}}{d \mathrm{x}} & =\frac{1}{2 \sqrt{\log \left\{\sin \left(\dfrac{\mathrm{x}^{3}}{3}-1\right)\right\}}} \cdot \frac{1}{\sin \left(\dfrac{\mathrm{x}^{3}}{3}-1\right)} \cdot \cos \left(\frac{\mathrm{x}^{3}}{3}-1\right) \cdot \frac{3 \mathrm{x}^{2}}{3} \\
& =\frac{\mathrm{x}^{2} \cot \left(\dfrac{\mathrm{x}^{3}}{3}-1\right)}{2 \sqrt{\log \left\{\sin \left(\dfrac{\mathrm{x}^{3}}{3}-1\right)\right\}}}
\end{aligned}
\]
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.