Let f (x) = g (x) h (x), g (10) = - 4, h (10) = 560, g' (10) = 0, and h' (10) = 35. find f' (10)

This question has extraneous info to trick you.

f (x) = g (x) h (x) ⇒ f' (x) = g' (x) h' (x). Letting x = 10, we get f' (10) = g' (10) h' (10). then just plug in the values provided. g (10) and h (10) are there to throw you off, just use g' (10) and h' (10).

So f' (10), pronounced "eff prime of ten", = 0 * 35 = 0.

If the question were asking for f (10) instead of f' (10) then you would use g (10) and h (10), ⇒-4*560=90.