Product Rule & Quotient Rule

Product Rule: d/dx[f·g] = f'·g + f·g'

"First times derivative of second, plus second times derivative of first."

Example: d/dx[x² · sin x] = 2x · sin x + x² · cos x

Quotient Rule: d/dx[f/g] = (f'·g - f·g') / g²

"Low d-high minus high d-low, over low squared."

Example: d/dx[sin x / x²] = (cos x · x² - sin x · 2x) / x⁴

Tip: The quotient rule is error-prone. If possible, rewrite the fraction as a product: f/g = f · g⁻¹ and use the product rule + chain rule instead. Fewer sign errors.

Both rules appear on every AP exam. Practice until they're automatic.

Reference:

Wikipedia: Product Rule

https://en.wikipedia.org/wiki/Product_rule