Derivative Help?

Question

How do I find the derivative of
y=(-x^2-6x-5)/(x+3)^2 in its simplest form?

Answer 1

The function y = (- x² - 6x - 5)/(x + 3)²

Simplify the function.

y = - (x² + 6x + 5)/(x + 3)²

y = - (x² + 6x + 9 - 4)/(x + 3)²

y = - [(x + 3)² - 4]/(x + 3)²

y = - (x + 3)²/(x + 3)² + [4/(x + 3)²]

y = - 1 + [4/(x + 3)²]

y = - 1 + 4(x + 3)^{- 2}

Differentiating on each with respect to x.

Apply the formulae d/dx(xⁿ ) = nx^n-1

d/dx(constant) = 0

y = 4(- 2)(x + 3)^{- 2 - 1}

y' = - 8 (x + 3)^{- 3}

y' = - 8/(x + 3)³