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Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 21 maths textbook solution

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Answer: e^{3 x} \cos 2 x

Hint: You must know the rules of solving exponential and trigonometric functions.

Given: e^{3 x} \cos 2 x


Let  y=e^{3 x} \cos 2 x

Differentiating with respect to x

\frac{d y}{d x}=\frac{d}{d x} e^{3 x} \cos 2 x

\frac{d y}{d x}=e^{3 x} \times \frac{d}{d x}(\cos 2 x)+\cos 2 x \frac{d}{d x}\left(e^{3 x}\right)

\frac{d y}{d x}=e^{3 x} \times(-\sin 2 x) \frac{d}{d x}(2 x)+\cos 2 x e^{3 x} \frac{d}{d x}(3 x)

\begin{aligned} &\frac{d y}{d x}=-2 e^{3 x} \sin 2 x+3 e^{3 x} \cos 2 x \\ &\frac{d y}{d x}=e^{3 x}[3 \cos 2 x-2 \sin 2 x] \end{aligned}

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