Given that f(x)=|U| where U is a function of x. Find f'(x)

Question

derivative of functions

Answer 1

If f(x)=|U| then (f(x))^2=U^2 and differentiating we have:

2f(x)f'(x)=2UU'

f'(x)=UU'/f(x)=UU'/|U|. Therefore f'(x)=-U' or U'. Whether this is positive or negative will depend on x. There is also the possibility that the derivative is undefined for particular values of x where U=0.

EXAMPLE

U=3-2x. The graph of U is V-shaped. When x=3/2, U=0 so f(x)=0 and f'(x) is not defined at x=3/2.

When x<3/2 the gradient U'=-2 and when x>3/2 U'=2.

Comments

Thank you very much.