What's the derivative of {sqrt (2x)} ?

[urbantrained]

I'm told that you don't need the product rule, or chain rule, or quotient rule to work it out. Can anyone show the workings as well please...?

 

[HallsofIvy]

I don't see anyway to find the derivative of √(2x) without using the chain rule (because of the "2", not the "√").

Write f(x)= (2x)^1/2 and use the "power" rule:

f'(x)= (1/2)(2x)^1/2-1(2x)'
= (1/2)(2x)^-1/2(2)
= 1/√(2x)

 

[Hurkyl]

√(2x) = √2 √x

You can take it from here using the power rule and the scalar multiple rule.

 

[chroot]

I love when you to Alfred E. Newmans fight it out.

- Warren

 

[Hurkyl]

You must be mad!

 

[HallsofIvy]

Hurkyl
ã(2x) = ã2 ãx

You can take it from here using the power rule and the scalar multiple rule.

Oh, well, if want to do it the EASY way!