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.
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