Calculus Book: pp 119-129

Question 1

product rule

Answer 1

• Suppose we want to differentiate f(x) = x2 sin(x). By using the product rule, one gets the derivative f′(x) = 2x sin(x) + x2 cos(x) (since the derivative of x2 is 2x and the derivative of the sine function is the cosine function). … This, combined with the sum rule for derivatives, shows that differentiation is linear.