Question

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

Answer 1

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".