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

• urbantrained
In summary, to find the derivative of &radic;(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 &radic;2 &radic;x. This method does not require the product, chain, or quotient rule. However, there may be alternative methods that use these rules.

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...?

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

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)

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

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

- Warren

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.