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

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Answer 1 · 2016-11-18T19:51:11

Please see the 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)#