MCQ
If $y = {\log _{\sin \,x}}\left( {\tan \,x} \right)$ , then ${\left( {\frac{{dy}}{{dx}}} \right)_{\pi /4}}$ is equal to
- A$\frac{4}{{\ln \,2}}$
- B$-4\ ln\ 2$
- ✓$\frac{{ - 4}}{{\ln \,2}}$
- D$4\ ln\ 2$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{(\log \sin \mathrm{x})\left(\frac{\sec ^{2} \mathrm{x}}{\tan \mathrm{x}}\right)-(\log \tan \mathrm{x})(\cot \mathrm{x})}{(\log \sin \mathrm{x})^{2}}$
or ${\left( {\frac{{dy}}{{dx}}} \right)_{\pi /4}} = \frac{{ - 4}}{{\log 2}}$ (On simplification)
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.