Proof that a function composition is differentiable

[Hernaner28]

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!

 

[SammyS]

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!

It does appear to be that simple, so I suppose that means, that you are wrong about it not being that simple.

Now, calculate g'(1) .

 

[Hernaner28]

Thanks! ;)