What is the product rule in differentiation?
The product rule is a special rule that exists for differentiating products of two (or more) functions. It states: If y=uv, then dy/dx= u(dv/dx) + v(du/dx). So when we have a product to differentiate we can use this formula.For example, suppose we want to differentiate y=x2(cos3x). In this question u=x2 and our v=cos(3x). So following the formula, our first step is to differentiate the u and v terms. du/dx=2x and dv/dx= -3sin(3x). We now put all these results into the given formula:dy/dx= u(dv/dx) + v(du/dx) = x2 x (-3sin3x) + 2x x cos3x We can tidy this answer up by noticing there is a common factor of x giving us this as a final answer: dy/dx= x(-3xsin3x+ 2cos3x )
