How do I differentiate f(x) = (x + 3)2?
There are three ways:
a. Expand the brackets f(x) = x2 + 6x + 9 therefore f '(x) = 2x + 6
OR
b. Use the Chain Rule f(x) = (x + 3)2 therefore f '(x) = 2(x + 3). 1 = 2x + 6
OR
c. Use the Product Rule f(x) = (x + 3)(x + 3) therefore f '(x) = (x + 3).1 + 1.(x + 3) = 2x + 6
Take your pick!
If f(x) = u(x) . v(x) why doesn't f '(x) = u '(x). v '(x)?
A proof of the product rule will answer this question.
