Question

How do you use the chain rule to differentiate `root11(-4x)`?

Answer 1

Please see the explanation.

Explanation:

Rewrite as: `f(x) = (-4x)^(1/11)`

The chain rule is: `(d(f(u(x))))/dx = (df(u))/(du)(du)/dx`

Let `u = -4x`, then:

`(du)/dx = -4, f(u) = u^(1/11), and (d(f(u)))/(du) = (1/11)u^(-10/11)`

Substituting into the chain rule:

`(d(f(u(x))))/dx = ((1/11)u^(-10/11))(-4)`

`(d(f(u(x))))/dx = (-4/11)u^(-10/11)`

Reverse the substitution:

`(d(f(u(x))))/dx = (-4/11)(-4x)^(-10/11)`