The discussion centers on proving the differentiability of the function g(x) = f(x)Arctg(f(x)) at x = 1, given that f: R -> R is differentiable with f(1) = 1 and f'(1) = 2. Participants confirm that the differentiability of g can be established through the product and composition rules of differentiation. The calculation of g'(1) is also requested, emphasizing the need for clarity in applying these differentiation principles.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation, as well as educators seeking to clarify concepts related to function composition and differentiability.
It does appear to be that simple, so I suppose that means, that you are wrong about it not being that simple.Hernaner28 said:Homework Statement
Let f:R->R, differentiable, f(1)=1 and f'(1)=2.
Homework Equations
Prove that g:R->R such that g(x)=f(x)Arctg(f(x)) is differentiable in x=1 and calculate g'(1)
The Attempt at a Solution
I would prove it saying that if a function is differentiable then the product and composition it's differentiable, but I don't think is that simple, am I wrong?
Thanks!