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  • need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 23

need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 23

Answers (1)

Answer: 3 e^{\tan 3 x} \sec ^{2} 3 x

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

Given: e^{\tan 3 x}

Solution:

Let  y=e^{\tan 3 x}

Differentiating with respect to x

\frac{d y}{d x}=\frac{d}{d x}\left(e^{\tan 3 x}\right)

\frac{d y}{d x}=e^{\tan 3 x} \frac{d}{d x}(\tan 3 x)                         \left[\therefore \frac{d}{d x} e^{x}=e^{x}\right] e^{a x}=e^{x} \frac{d}{d x}(a)

\frac{d y}{d x}=e^{\tan 3 x} \sec ^{2} 3 x \times \frac{d}{d x}(3 x)                \left[\therefore \frac{d}{d x} \tan a x=s \sec ^{2} a x\right]

\begin{aligned} &\frac{d y}{d x}=e^{\tan 3 x} \cdot \sec ^{2} 3 x \times 3 \\ &\frac{d y}{d x}=3 e^{\tan 3 x} \sec ^{2} 3 x \end{aligned}                    \left[\therefore \frac{d}{d x} \tan a x=a \sec ^{2} a x\right]

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