Thread: d/dx f[1/g(x)] ?

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,

Originally Posted by SportfreundeKeaneKent

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 ^

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 :
, for


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.

Originally Posted by SportfreundeKeaneKent

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 ^

Originally Posted by Moo

Hello,



Yes, this is the answer

[snip]

The derivative of with respect to x is so I think there might be a negative in there somewhere, too .....