Question

What is the derivative of `2 sqrtx` ?

Answer 1

In general if `f(x) = a*x^b`
`color(white)("XXXX")` `(d f)/(dx) = b*a*x^(b-1)`

Since `f(x) = 2sqrt(x)`
is the same as `f(x) = 2*x^(1/2)`
`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")` `(d f)/(dx) = (1/2) * 2 * x^(-1/2)`

`color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")` `color(white)("XXXX")` `=1/sqrt(x)`