A) \[2\sqrt{2}a\]
B) \[\sqrt{2}a\]
C) \[\text{si}{{\text{n}}^{\text{2}}}\beta =\text{ 3si}{{\text{n}}^{\text{2}}}\theta \]
D) \[\text{co}{{\text{s}}^{\text{2}}}\theta \]
Correct Answer: A
Solution :
Given, \[y=\sin \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\] On differentiating both sides w.r.t. x, we get \[\frac{dy}{dx}=\cos \left[ \log \left( \frac{2x+3}{3-2x} \right) \right].\frac{3-2x}{2x+3}\] \[\frac{(3-2x)2-(2x+3)(-2)}{{{(3-2x)}^{2}}}\] \[\Rightarrow \] \[\frac{dy}{dx}=\cos \left[ \log \left( \frac{2x+3}{3-2x} \right) \right].\frac{3-2x}{2x+3}.\frac{12}{{{(3-2x)}^{2}}}\] \[=\frac{12}{9-4{{x}^{2}}}.\cos \left[ \log \left( \frac{2x+3}{3-2x} \right) \right]\]You need to login to perform this action.
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