H2 Maths 5.1 - Product, Quotient, and Chain Rules (Combined)

What you will learn

• Differentiate f(x) = x^2 e^(3 x) / ln(x); the whole is a quotient, the numerator is a product, and e^(3 x) needs the chain rule.
• Numerator: u = x^2 e^(3 x), u' = 2 x e^(3 x) + 3 x^2 e^(3 x) = e^(3 x)(2 x + 3 x^2).
• Denominator: v = ln x, v' = 1 / x; apply f' = (u' v - u v') / v^2.