Question

How do you find the derivative of the function `f(x) = x + x^(1/2)`?

Answer 1

By the first derivative rule (and the simplest one): be `f(x)=x^n`, then `(df(x))/(dx)=n*x^(n-1)`

Explanation:

`(df(x))/(dx)=1*x^0+(1/2)*x^(-1/2)`

As everything times zero is zero and following a power rule that states that `a^-n=1/a^n`, we get:

`(df(x))/(dx)=1+1/(2x^(1/2))`