Coin Toss Problem Derivative of (1-p)^3

[Nate_Carpenter]

In solving the coin toss problem, the instructor take the derivative of (1-p)^3. At first, it makes sense he comes up with 3(1-p)^2. We already did something similar with the power line problem where he took each area equation and applied the same derivative rule.

However, he then says we need to take the derivative of the inside which is -1, and apply the chain rule coming up with (1-p)^3(-1).

Why is this extra step of taking the inside derivative necessary when it wasn’t necessary for the power line example which simply completed the first step: (x-a)^2 → 2(x-a) ?

[balaji.ambresh]

This is because
\frac{d}{dx} (x-a) = 1

[SNaveenMathew]

Another approach: \frac{\partial (1-p)^3}{\partial p} = \frac{\partial (1-p)^3}{\partial (1-p)} * \frac{\partial (1-p)}{\partial p} = 3(1-p)^2*(-1)