# If #f(x) =-sqrt(2x-1) # and #g(x) = (2-1/x)^2 #, what is #f'(g(x)) #?

##### 1 Answer

The question is asking, "what is the equation for the derivative of

So we need to do two things: **(1)** Find the general derivative of **(2)** Plug in

**Step (1):**

If

then

by use of both the power rule and the chain rule.

This is the general derivative of

**Step (2):**

Now, we plug in the input

Depending on your teacher, this is likely as far as you'll need to go.

## Bonus:

Please note: The domain of

(Slightly more limiting than the domain of just

The domain of

That means the domain of this composite function *both* of these restrictions. Luckily, that's pretty easy, considering the domain of