OCR A Level Maths - Differentiation Rules

The function $ {x ^ 2} \, (x−1) $ is a product of $ {x ^ 2} $ and $ (x−1) $. The derivative of $ {x ^ 2} $ is $ 2x $ and the derivative of $ (x−1) $ is $ 1 $. So, is the derivative of $ {x ^ 2} \, (x−1) $ equal to $ 2x(1) = 2x $, or $ 2x + 1 $, or something else?

This display allows you to visualise the curve $ {x ^ 2} \, (x − 1) $, as well as many other products of functions. You can use it to visualise the "Product Rule" which defines how gradient functions are derived for products of functions.

The connection between a function $ h(x) $ and it derivative $ h'(x) $ is much harder to see when the function $ h(x) $ is a quotient of two other functions.

This display allows you to visualise the curve $ { x \over x + 1 } $, as well as many other quotients of functions. You can use it to visualise the "Quotient Rule" which defines how gradient functions are derived for quotients of functions.