HELP WITH PRODUCT RULE: Suppose that u and v are differentiable at x = 2

Question

Suppose that u and v are differentiable at x = 2 and that u(2)=4, v(2)=-9, u'(2)=5, and v'(2)=3

a. Find d/dx(6uv) at x=2

b. Find d/dx(u/v) at x=2

Answer 1

The product rule of derivatives of two functions u and v is defined as u'v + v'u. The values are given for x = 2, so input and evaluate. The quotient rule of derivatives is defined as (u'v + v'u)/v^2.