Product rule

[dcgirl16]

if im trying to find the derivative of y=3x(x-4)(x+2) do i multipy the 3x through first or go right to the product rule ad if i do multiply it through do i multipy it through both terms
(3x^2-12x)(3x^2+6x) or
3(3x^2-12x)(x+2)

 

[berkeman]

Thread moved to Homework Help, Calculus. dcgirl16, homework and coursework questions belong in the appropriate Homework Help forum, not in the main forums.

And on your question, for me it's easiest to multiply it out first before taking the derivative, at least in this particular problem.

 

[justine411]

multiply everything out, like you did in your first suggestion, but then multiply those together ((3x^2-12x)(3x^2+6x)) then take the derivative.

 

[Dick]

multiply everything out, like you did in your first suggestion, but then multiply those together ((3x^2-12x)(3x^2+6x)) then take the derivative.

DO NOT MULTIPLY BOTH FACTORS BY THE FIRST FACTOR. Multiplication doesn't work that way! Jeez! And you should get the same answer no matter how you do it. If you are dubious it's worth trying both ways.

 

[drpizza]

Also, have you derived the product rule for the product of 3 factors yet? Generally, it's nicer to simplify before applying derivative rules than it is to simplify after taking the derivatives.