F(x)=IsinxI what is F'(x) without making it as composite function

Question

akshay_budhkar · Answer

what i believe is you need to open the MOD in different cases and then differentiate it in the given domains with the proper signs

akshay_budhkar · Answer

yea right where ever the function changes sign F"(x) doesn't exist.. as it is not differentiable at points where the slope changes and slope chnges at x=k(pie)

jamesj · Answer

It is most definitely not true that F'(x) = | cos x |

Sketch the graph of | sin x | .  Then you can see what the derivative has to be.  Once you have a sense of it, then figure that out analytically.

zarkon · Answer

$$F'(x)=\frac{\sin(x)}{|\sin(x)|}\cos(x)$$

jamesj · Answer

One way you can get to Zarkon's answer is to write
$$F(x) = | \sin x| = \sqrt{\sin^2 x}$$
Now carefully differentiate.