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

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

Answers (1)

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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