How do you differentiate #y=(6x^2 + 2x)^3#?

2 Answers
Noah G
Mar 7, 2018

#dy/dx= 3(12x + 2)(6x^2 + 2x)^2#

Explanation:

Don't bother expanding, just use the chain rule. Let #u = 6x^2+2x#. Then #du = 12x + 2#. This also means that #y = u^3#., or #y = 3u^2#.

#dy/dx = (12x +2)3(6x^2 + 2x)^2#

#dy/dx= 3(12x + 2)(6x^2 + 2x)^2#

Hopefully this helps!

Bryson
Mar 7, 2018

#3(6x^2+2x)^2(12x+2)#

Explanation:

Applying the chain rule we arrive at the consensus that #d/dx f(g(x)) = f'(g(x))*g'(x)#
we identify the variables within our problem and define that #f(x) = x^3# and
#f'(x)=3(x)^2#
#g(x) = 6x^2+2x#
combining the functions together with recieve the original function
#g'(x)=12x+2# using the power rule #Px^(P-1)#
from this point we plug out g(x) and f(x) functions into our rules of derivatives.

Related questions
See all questions in Chain Rule
Impact of this question
5062 views around the world
You can reuse this answer
Creative Commons License