Question

How do you differentiate `f(x)=(x^3-5x)^4`?

Answer 1

Use the chain rule, `(df)/dx = (df)/(du)(du)/(dx)`

Explanation:

Let `u = x^3 - 5x`, then, `f(u) = u^4`, `(df)/(du) = 4u^3`, and `(du)/(dx) = 3x² - 5`

Substituting this into the chain rule:

`(df)/dx = 4u³(3x² - 5)`

Reverse the u substitution:

`(df)/dx = 4(x^3 - 5x)³(3x² - 5)`