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

  • Thread starter urbantrained
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In summary, to find the derivative of √(2x), you can use the power rule by writing f(x)= (2x)1/2 and using the "power" rule. Then, you can use the scalar multiple rule to simplify the equation and get the final answer of √2 √x. This method does not require the product, chain, or quotient rule. However, there may be alternative methods that use these rules.
  • #1

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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  • #2
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)
 
  • #3
√(2x) = √2 √x

You can take it from here using the power rule and the scalar multiple rule.
 
  • #4
I love when you to Alfred E. Newmans fight it out.

- Warren
 
  • #5
You must be mad!
 
  • #6
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!
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It tells us how fast a function is changing at that point.

How do you find the derivative of a function?

The derivative of a function is found by taking the limit of the difference quotient as the change in x approaches 0. In simpler terms, it is found by taking the slope of the tangent line at a specific point on the function.

What is the chain rule?

The chain rule is a rule used in calculus to find the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

What is the derivative of a square root?

The derivative of a square root function is equal to 1 over 2 times the square root of the original function. In other words, it is equal to half the original function raised to the power of -1/2.

What is the derivative of √(2x)?

The derivative of √(2x) is equal to 1 over 2 times the square root of 2x. This can also be written as 1 over 2√(2x). In general, the derivative of √(ax) would be 1 over 2 times the square root of ax.

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