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

2 Answers
Mar 7, 2018

Answer:

#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!

Mar 7, 2018

Answer:

#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.