Extended Product Rule The Product Rule can be extended to the product of three functions.

(a) Use the Product Rule twice to prove that if f, g, and h are differentiable, then (fgh)' = f'gh + fg'h + fgh'.

(b) Taking f = g = h in part (a), show that

(c) Use part (b) to differentiate y = e^3ϰ.

Transcribed Image Text:

d [f(x)]³ = 3[f(x)]'f'(x) dx