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Please solve RD Sharma class 12 chapter 10 Differentiation exercise Fill in the blanks question  26 maths textbook solution

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Answer: the correct answer is \frac{1}{\sqrt{2}}

Hint:

Given: f^{1}(1)=2 \text { and } g^{1}(\sqrt{2})=4

Solution:  

\begin{aligned} &y=f(\tan x) \text { and } z=g(\sec x) \\\\ &\frac{d y}{d x}=f^{\prime}(\tan x) \sec ^{2} x \text { and } \frac{d z}{d x}=g^{\prime}(\sec x) \cdot \sec x+\tan x \end{aligned}

\begin{aligned} &\frac{d y}{d z}=\frac{f^{1}(\tan x) \cdot \sec ^{2} x}{g^{1}(\sec x) \cdot \sec x \tan x} \\\\ &\frac{d y}{d z}=\frac{f^{\prime}(1) \cdot(\sqrt{2})^{2}}{g^{\prime}(\sqrt{2}) \cdot(\sqrt{2})}=\frac{1}{\sqrt{2}} \end{aligned}

So the answer is \frac{1}{\sqrt{2}}

 

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