Given a derivative, find other ones

[Jacobpm64]

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?
(c) k ((1/4)x) when x = 4?


Here is my work:
k'(1) = 2

(a) k'(2x) = ?
k'(2(1/2)) = ?
k'(1) = 2

(b) k'(x+1) = ?
k'(0+1) = ?
k'(1) = 2

(c) k'((1/4)x) = ?
k'((1/4)(4)) = ?
k'(1) = 2

Is the answer for every question 2?

I just find it strange that this question would be that easy, so naturally I think I approached it incorrectly.

Please tell me if it is correct.

Thanks.

 

[courtrigrad]

no you have to use the chain rule.

the derivative of $$k(2x)$$ is $$k'(2x)(2)$$ So its $$k'(1)(2) = 4$$

 

[Jacobpm64]

All right, let's try this again:

(a) $$k'(2x) = k'(2x)(2) = k'(1)(2) = 4$$

(b) $$k'(x+1) = k'(x+1)(1) = k'(1)(1) = 2$$

(c) $$k'(\frac{1}{4}x) = k'(\frac{1}{4}x)(\frac{1}{4}) = k'(1)(\frac{1}{4}) = \frac{1}{2}$$

 

[courtrigrad]

yes that is correct