Question

suppose u and v are functions of x that are differentiable at x=2 and
that u(2) =3, u'(2) = -4, v(2) = 1, and v'(2)

find values of derivatives at x = 2

(d/dx)(uv) = ?

I would like to know how to set this up because I'm only used to getting problems that want the d/dx given ex: y=2x+1 so I was confused for this

The answer is 2 but how do I set this up?

Answer 1

This is just the product rule.

d/dx(uv) = du/dx * v + u * dv/dx

when x=2,

d/dx(uv) = (-4)(1) + (3)(2) = -4+6 = 2