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

2 Answers
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!

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.