derivative questions!?

Question

If the derivative of y = k(x) equals 2 when x = 1, what is the derivative of
a. k(2x) when x = 1/2
b. k(x+1) when x = 0

Answer 1

Let f(x) = k(2x) and g(x) = k(x+1). According to the chain rule, it follows f'(x) = k'(2x)* 2 and g'(x) =k'(x+1)

So, f'(1/2) = 2k'(1) = 2 * 2 = 4 and g'(0) = k'(1) = 2