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]