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JEE MATHEMATICS MCQ: DIFFERENTIATION

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If y=f(2x+33−2x)y = f\left( {\frac{{2x + 3}}{{3 - 2x}}} \right) and f(x)=sin⁡(log⁡x),f\left( x \right) = \sin (\log x), then dydx\frac{{dy}}{{dx}} is equal to
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Correct option: A
129−4x2cos⁡{log⁡(2x+33−2x)}\frac{{12}}{{9 - 4{x^2}}}\cos \left\{ {\log \left( {\frac{{2x + 3}}{{3 - 2x}}} \right)} \right\}
Option A (129−4x2cos⁡{log⁡(2x+33−2x)}\frac{{12}}{{9 - 4{x^2}}}\cos \left\{ {\log \left( {\frac{{2x + 3}}{{3 - 2x}}} \right)} \right\}) is correct because it follows from applying the chain rule to differentiate the composite function.

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