Product Rule #
$$[g \cdot h]' = g' \cdot h + g \cdot h'$$Quotient Rule #
$$\left[\frac{g}{h}\right]' = \frac{g' \cdot h - g \cdot h'}{h^2}$$Example (Product): \(f = x^2 \sin x\) #
\(f’ = 2x \sin x + x^2 \cos x\)
Example (Quotient): \(f = \frac{x^2}{x+1}\) #
\(f’ = \frac{2x(x+1) - x^2}{(x+1)^2} = \frac{x^2+2x}{(x+1)^2}\)
Common mistakes: ❌ \((g/h)’ \neq g’/h’\). ❌ Forgetting the minus sign. ❌ Forgetting to square the denominator.
Reply by Email