Question

Differentiate y = (1-x)(x² - 4)²​

Answer 1

Below in bold.

Explanation:

Using the product rule:

dy/dx = (1 - x)* d (x² - 4)²​/dx + (x² - 4)² * -1

Differentiate (x² - 4)²​:-

Using the Chain Rule:

this = 2(x² - 4) * 2x

= 4x(x² - 4)

So substituting the above we have

dy/dx = (1 - x)4x(x² - 4) + (x² - 4)² * -1

= (1 - x)4x(x² - 4) - (x² - 4)²

= (x² - 4)(4x(1 - x) - (x² - 4))

= (x² - 4)(4x - 4x² - x² + 4)

= (x² - 4)(-5x² + 4x + 4)

= -(x² - 4)(5x² - 4x - 4) Answer

this expanded is

-5x⁴ + 4x³ + 24x² - 16x - 16 Answer.