When the first function is multiplied by the derivative of the second plus the second function multiplied by the derivative of the first function, then the product rule is given. Here we take u constant in the first term and v constant in the second term.
Question: Differentiate the function: (x2 + 3)(5x + 4)
Given function is: (x2 + 3)(5x + 4)
Here u = (x2 + 3) and v = (5x + 4)
Using product rule,
= (x2 + 3) 5 + (5x + 4) 2x
= 5x2 + 15 + 10x2 + 8x
= 15x2 + 8x + 15