Question

How do you find the derivative of `y =sqrt(2x)`?

Answer 1

First, convert the square root to its exponential equivalent. Then apply the Chain and Power Rules. Next simplify the function. Lastly, convert the negative exponents back to square roots.

`y=sqrt(2x)`

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

`y'=(1/2)(2x)^((1/2-1))*2`

`y'=(1/2)(2x)^((-1/2))*2`

`y'=(2/2)(2x)^((-1/2))`

`y'=(1)(2x)^((-1/2))`

`y'=(2x)^((-1/2))`

`y'=1/sqrt(2x)`