Question

If f(x) = sin$\left|x\right|$ then the value of $\frac{df}{dx}$ at x = $-\frac{\pi }{4}$ is

• A. 0
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{-1}{\sqrt{2}}$
• D. 1

Answer 1

The correct option is C $\frac{-1}{\sqrt{2}}$

f(x) = sin$\left|x\right|$

$\frac{df}{dx}=cos\left|x\right|.\frac{\left|x\right|}{x}$

= $\{\begin{array}{c}cos(-x).(-1),x<0\\ cos\left(x\right).\left(1\right),x>0\end{array}$

=$\{\begin{array}{c}-cosx,x<0\\ cosx,x>0\end{array}$

So ${\left(\frac{df}{dx}\right)}_{x=\frac{-\pi }{4}}=-cos\left(\frac{-\pi }{4}\right)=\frac{-1}{\sqrt{2}}$