Given y = f (u) and u = g (x), find dy/dx = f' (g (x)) g' (x).

Due to the sensitivity of writing f (u), it's derivatives, and other terms that contain it, I replaced f (u) by h (u).

Step-by-step explanation:

Answer:

dy/dx = (dy/dw) * (dw/dx)

= h' (g (x)) g' (x)

Step-by-step explanation:

Given y = h (w), and w = g (x)

dy/dx can be obtained by applying Chain Rule by finding dy/du and du/dx, and multiplying them. That is,

dy/dx = (dy/du) * (du/dx)

y = h (u)

dy/du = h' (u)

u = g (x)

dw/dx = g' (x)

Since w = g (x), we can write h' (u) as h' (g (x)).

So,

dy/du = h' (g (x))

dy/dx = (dy/du) * (du/dx)

= h' (g (x)) * g' (x)

= h' (g (x)) g' (x)

Which is exactly what we are trying to obtained if we replaced "h" by "f".