Question

What is the derivative of `sqrt(2x)`?

Answer 1

`1/sqrt(2x)`

Explanation:

The function can be rewritten as

`(2x)^(1/2)`

To differentiate this, use the power rule and chain rule.

`d/dx[(2x)^(1/2)]=1/2(2x)^(-1/2)d/dx[2x]`

Differentiating with the power rule gives the `1/2(2x)^(-1/2)` part, and through the chain rule you must multiply this by the derivative of the internal function, which is `2x`.

This gives:

`d/dx[(2x)^(1/2)]=1/2(2x)^(-1/2)(2)`

The `2`s will cancel.

`d/dx[(2x)^(1/2)]=(2x)^(-1/2)=1/(2x)^(1/2)=1/sqrt(2x)`