Q:

find the derivative using quotient rule y = (x + 1)^2(x2 + 1)^-3 step by step pls

Accepted Solution

A:
let f(x)=g(x)/h(x)
The quotient rule states that:
f'(x)=[g'(x)h(x)-g(x)h'(x)]/[h(x)]²
From the expression given:
y = (x + 1)^2(x2 + 1)^-3
y=(x+1)²/(x²+1)³
where:
g(x)=(x+1)²
g'(x)=2(x+1)

h(x)=(x²+1)³
h'(x)=6x(x+1)²
hence to get the derivative of y we substitute in the formula:
y'=[2(x+1)(x²+1)³-6x(x+1)²(x+1)²]/[(x²+1)^6]
simplifying the above we get:
y[2(x+1)(x²+1)³-6x(x+1)^4]/[(x²+1)^6]