Need help with the Chain Rule

[Incog]

1. The problem statement, all variables and given/known data

A: Write f(x) = \sqrt{5-x^{2}} as a composite of two functions.

B: Use the Chain Rule to find the derivative of f(x) = \sqrt{5-x^{2}}

2. Relevant equations

Chain Rule:

y`= \frac{dy}{du} \frac{du}{dx}

3. The attempt at a solution

A:

y = \sqrt{u}
u = 5 - x^{2}


B:

This is where I get confused. I don't understand what's meant by "d" and what's meant by "y", "u", and "x".

I know the two du's cancel out in the Chain Rule so you're left with:

y`= (dy)(dx)

Does this mean the derivative of y times the derivative of x? And if so, how do you know what y and x are?

[Doc Al]

y = \sqrt{u}
u = 5 - x^{2}
Good!
This is where I get confused. I don't understand what's meant by "d" and what's meant by "y", "u", and "x".
dy/dx is just notation for: take the derivative of the function y with respect to the variable x.

I know the two du's cancel out in the Chain Rule so you're left with:

y`= (dy)(dx)
Not exactly. y' = dy/dx.

The point is that you want to find dy/dx and that dy/dx = (dy/du)*(du/dx). And it's easy to calculate the derivatives dy/du and du/dx.

[Incog]

dy/dx is just notation for: take the derivative of the function y with respect to the variable x.


Thanks. That cleared the confusion. :cool: