find derivative of function

Question

y=(4x+8)^2

Answer 1

Given that y=(4x+8)²

Apply derivative each side with respective'x'

dy/dx=d/dx(4x+8)²

Power Rule of Derivative: (d/dx)(xⁿ)=n.x^n-1

dy/dx=2(4x+8)d/dx(4x+8)     

dy/dx=8x+16[d/dx(4x+8)]           derivative of inner terms

(d/dx)(nx)=n and (d/dx)(constant)=0

dy/dx=(8x+16)4

dy/dx=32x + 64.

Take out common term 32.

dy/dx=32(x + 2)

Therefore the derivative of y is 32(x + 2).