Question

[Calc 1] An explanation on how to best solve this. I've been stuck trying to use chain rule

Answer 1

Answer:

  G'(y) = 4y^7(y+4)/(y+2)^5

Step-by-step explanation:

Work it a piece at a time.

Define z = y^2/(y+2). Then your derivative is found from the power rule as ...

  G = z^4

  G' = 4z^3·z'

Now, define z = u/v. Then your derivative is found using the quotient rule:

  z' = (vu' -uv')/v^2 = ((y+2)(2y) -(y^2)(1))/(y+2)^2

Putting this together we have ...

  $G'(y)=4\left(\dfrac{y^2}{y+2}\right)^3\cdot\dfrac{y^2+4y}{(y+2)^2}\\\\\boxed{G'(y)=\dfrac{4y^8+16y^7}{(y+2)^5}}$