Question

What is the derivative of `sqrt(2x-1)`?

Answer 1

`1/(sqrt(2x-1))`

Explanation:

This is a case of using the power rule and the chain rule.

First, we note that `sqrt(2x-1)` can be rewritten as `(2x-1)^(1/2)`.
Now we can apply the power rule, where we multiply the function by the exponent then decrease the exponent by one:
`d/dx(2x-1)^(1/2)=(1/2)(2x-1)^(1/2-1)`
`=1/2(2x-1)^(-1/2)`

Then we apply the chain rule, which tells us to multiply this result by the derivative of the "inside" function. In our case, the "inside" function is `2x-1` (because it is inside the square root), and its derivative is simply `2`. Our final derivative now becomes:
`1/2(2x-1)^(-1/2)*2=(2x-1)^(-1/2)`

In radical form, this is `1/(sqrt(2x-1))`.