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  • Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 9 maths textbook solution

Please solve RD Sharma class 12 chapter Differentiation exercise 10.2 question 9 maths textbook solution

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Answer: \frac{5 \pi}{180} \sec ^{2}\left(5 x^{\circ}\right)

Hint: You must know the rules of solving derivative of logarithm function.

Given: \tan 5 x^{\circ}

Solution:

Let  y=\tan 5 x^{\circ}  or y=\left(\tan 5 x \times \frac{\pi}{180}\right)

Differentiating with respect to x

\frac{d y}{d x}=\frac{d y}{d x} \tan \left(5 x \times \frac{\pi}{180}\right)

\frac{d y}{d x}=\sec ^{2}\left(5 x \times \frac{\pi}{180}\right) \frac{d}{d x}\left(5 x \times \frac{\pi}{180}\right)             [  using chain rule ]

\begin{aligned} &\frac{d y}{d x}=\left(\frac{5 \pi}{180}\right) \sec ^{2}\left(5 x \times \frac{\pi}{180}\right) \\ &\frac{d y}{d x}=\frac{5 \pi}{180} \sec ^{2}\left(5 x^{\circ}\right) \end{aligned}

 

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