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  • Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question 11

Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  11

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

Hint: 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)

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

Solution:  

        f(x)=|\cos x|

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

\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^{1}\left(\frac{\pi}{2}\right) &=-\sin \frac{\pi}{2} \\ &=-\frac{1}{\sqrt{2}} \end{aligned}

 

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