A) 6 sin log (5)
B) 5 sin log (6)
C) 12 sin log (5)
D) 5 sin log (12)
E) 12 sin log (6)
Correct Answer: C
Solution :
\[\frac{dy}{dx}=f\left( \frac{2x+3}{3-2x} \right)\frac{d}{dx}\left( \frac{2x+3}{3-2x} \right)\] \[=\sin \log \left( \frac{2x+3}{3-2x} \right)\left( \frac{(3-2x)(2)-(2x+3)(-2)}{{{(3-2x)}^{2}}} \right)\] \[=\frac{12}{{{(3-2x)}^{2}}}\sin \left\{ \log \left( \frac{2x+3}{3-2x} \right) \right\}\] \[\therefore \] \[{{\left( \frac{dy}{dx} \right)}_{x=1}}=\frac{12}{{{(3-2)}^{2}}}.\sin \,\log 5\]
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