If anyone is still confused and wants to understand fully how to derive the product rule, check this lecture note from MIT OCW: ocw(dot)mit(dot)edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/1.-differentiation/part-a-definition-and-basic-rules/session-9-product-rule/MIT18_01SCF10_Ses9c.pdf####[]