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BCECE Engineering BCECE Engineering Solved Paper-2012

  • question_answer
    If\[f(x)=\sin (\log x)\]and \[y=f\left( \frac{2x+3}{3-2x} \right),\]then \[\frac{dy}{dx}\]is

    A)  \[\frac{9\cos (\log x)}{x{{(3-2x)}^{2}}}\]              

    B)         \[\frac{9\cos \left( \log \frac{2x+3}{3-2x} \right)}{x{{(3-2x)}^{2}}}\]

    C)         \[\frac{9\sin \left( \log \frac{2x+3}{3-2{{x}^{2}}} \right)}{{{(3-2x)}^{2}}}\]

    D)         None of the above

    Correct Answer: D

    Solution :

    \[y=f(t),\]where \[t=\frac{2x+3}{3-2x}\] \[\Rightarrow \]               \[\frac{dy}{dx}=f(t)\times \frac{dt}{dx}\]                 \[=\sin \left( \log \frac{2x+3}{3-2x} \right)\times \frac{12}{{{(3-2x)}^{2}}}\]


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