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  • Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question 14

Provide solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  14

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Answer: f^{1}\left(\frac{\pi}{4}\right)=\left(\frac{1}{\sqrt{2}}\right)

Hint:f^{1}(x)=\left(\begin{array}{cc} \sin x & 0 \leq x \leq \frac{\pi}{2} \\\\ -\sin x & \frac{\pi}{2}<x<\pi \end{array}\right)

Given: f(x)=|\sin x|

Solution:  

\begin{aligned} &f(x)=\left(\begin{array}{cc} \sin x & 0 \leq x \leq \frac{\pi}{2} \\\\ -\sin x & \frac{\pi}{2}<x<\pi \end{array}\right) \\\\ &f^{{}'}(x)=\left(\begin{array}{cc} \cos x & 0 \leq x \leq \frac{\pi}{2} \\\\ -\cos x & \frac{\pi}{2}<x<\pi \end{array}\right) \end{aligned}

\begin{aligned} f^{{}'} \frac{\pi}{2}=& \cos \frac{\pi}{4} \\\\ &=\frac{1}{\sqrt{2}} \end{aligned}

 

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