given d/dx [ f(2x) ] = f ' (x) and f ' (1) = 1, find f '(2)
a) 1/4
b) 1/2
c) 3/4
d) 3/2
e) 5/2

Question

given d/dx [ f(2x) ] = f ' (x) and f ' (1) = 1, find f '(2)
a) 1/4
b) 1/2
c) 3/4
d) 3/2
e) 5/2

zubhanwc3 · Answer

$$\frac{ d }{ dx }[f(2x)]=f'(x) $$ and $$f'(1)=1, $$ find $$f'(2)$$

zepdrix · Answer

Take the derivative of the left side, applying the chain rule:$$\Large\rm 2f'(2\color{orangered}{x})=f'(\color{orangered}{x})$$Understand that step?

zepdrix · Answer

Then if you evaluate this at x=1, you would be able to solve for f'(2) without too much trouble! :)$$\Large\rm 2f'(2\cdot\color{orangered}{1})=f'(\color{orangered}{1})$$

zubhanwc3 · Answer

so f'(2) is 2 i presume

zepdrix · Answer

So we have:$$\Large\rm 2f'(2)=f'(1)$$Yes?
Can we plug in any information from here?
And then solve for f'(2) somehow?

zubhanwc3 · Answer

by doing 2f'(2*2) = f'(2) so it would be 2, im just confirming.

zubhanwc3 · Answer

o, mb, i feel stupid now, its 1/2 because if we divide both sides by 2, f'(2) = f'(1)/2 which is 1/2

zepdrix · Answer

ya there we go! :)