find f'(2) given g(2)=3, h(2)=-1, h'(2)=4, and g'(2)=-2

Question

f(x)=g(x)h(x)

I'm just not understanding how to start this at all and what it wants me to derive when I don't know the function

Answer 1

You don't actually have to know the whole function to get its value at one point, if you have other useful information.

You can - and should! - look up the background to "Leibniz's law", but it says that

f(x)=g(x)h(x)
implies
f'(x)=g'(x)h(x) + g(x)h'(x)

Now, this is true for all x, but you only need the value for one x, and I think you can handle it from there.
f'

Answer 2

thanks so much!

Answer 3

You're very welcome, Bri. And do look up _why_ that is true sometime. It's quite neat.