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 ^
Hello,
Yes, this is the answer
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 :
$\displaystyle f(x)=\sqrt{x}$, for $\displaystyle x \in [0, \infty[$
$\displaystyle f'(x)=\frac{1}{2 \sqrt{x}}$
This is defined all over $\displaystyle ]0, \infty[$. But not in 0.
The function is not differentiable in 0.
But here you have to add that g(x) never annulates.