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  • Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Multiple choice question 28

Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Multiple choice question 28

Answers (1)

Answer:

        1

Hint:

        Differentiate the function w.r.t x

Given:

        y=\log \sqrt{\tan x}

Solution:  

        \begin{aligned} &y=\log \sqrt{\tan x} \\\\ &\frac{d y}{d x}=\frac{1}{\sqrt{\tan x}} \times \frac{d}{d x}(\sqrt{\tan x}) \end{aligned}

              =\frac{1}{\sqrt{\tan x}} \times \frac{1}{2 \sqrt{\tan x}} \times \frac{d}{d x}(\tan x)

        \frac{d y}{d x}=\frac{\sec ^{2} x}{2 \tan x}

Now

        \left(\frac{d y}{d x}\right)_{x=\frac{\pi}{4}}=\frac{\left(\sec \frac{\pi}{4}\right)^{2}}{2 \tan \left(\frac{\pi}{4}\right)}=\frac{2}{2 \times 1}=1

Posted by

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