How to take the derivative given a prime value.

Question

Suppose R '(1) = 10.

(a) If f(x) = R(8x),   find f ' (1/8)

 

So I am confused on what it is asking. What do I do. I thought I take the derivative but that would just get me r(8) and so 1/8 isnt used. I am just not sure what it is asking.

Answer 1

f'(x) = R'(8x)•8 by application of the chain rule.

 

f'(1/8) = R'(8•(1/8))•8 = R'(1)•8 = 10(8) = 80.