Question

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

Answer 1

`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!

Answer 2

`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.