I have a question stating:
Find d/dx f[1/g(x)]
g(x) and f(x) are differentiable. What exactly does this mean?
My solution is f'(1/g(x)*g'(x)/g(x)^2
Using the chain rule there ^
Differentiable means that you can differentiate the function. More generally, and in this case, it means that g'(x) and f'(x) exist. Here is an example :
This is defined all over . But not in 0.
The function is not differentiable in 0.
But here you have to add that g(x) never annulates.