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need solution for RD Sharma maths class 12 chapter Differentiation exercise 10.2 question 3

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Answer: \frac{\pi}{180} \sec ^{2}\left(x^{\circ}+45^{\circ}\right)

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

Given: \tan \left(x^{\circ}+45^{\circ}\right)


y=\tan \left(x^{\circ}+45^{\circ}\right)

y=\left[\tan (x+45) \cdot \frac{\pi}{180}\right]   ...To convert degree into radian multiply by \frac{\pi }{180}

Differentiating with respect to x,

\frac{d y}{d x}=\frac{d}{d x}\left[\tan (x+45) \cdot \frac{\pi}{180}\right]

\frac{d y}{d x}=\frac{\pi}{180} \cdot \sec ^{2}[\mathrm{x}+45] \times \frac{d}{d x}(x+45) \frac{\pi}{180}                   [ using chain rule]

\frac{d y}{d x}=\frac{\pi}{180} \sec ^{2}\left(x^{\circ}+45^{\circ}\right)

\text { So, } \frac{d}{d x}\left[\tan \left(x^{\circ}+45^{\circ}\right)\right]=\frac{\pi}{180} \sec ^{2}\left(x^{\circ}+45^{\circ}\right)



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