Question

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

Answer 1

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

Answer 2

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)

Answer 3

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.

Answer 4

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

Answer 5

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