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".
