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:

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".

so what is the question

step-by-step explanation:

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3