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

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SUMMARY

The derivative of the function f(x) = √(2x) can be calculated using the power rule without the need for the product, chain, or quotient rules. By rewriting the function as f(x) = (2x)^(1/2) and applying the power rule, the derivative is found to be f'(x) = √2 √x. This method simplifies the differentiation process while maintaining accuracy in the calculations.

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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...?
 
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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)
 
√(2x) = √2 √x

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

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