Question

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

Answer 1

The derivative of `sqrt(x)` is `1/(2sqrt(x))`.

Remember that we can rewrite surds like this in index notation. For this case, `sqrtx=x^(1/2)`.

Now we can simply use the power rule for differentiation, namely that `d/dx x^n=nx^(n-1)`. Let `n=1/2`. Therefore:

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

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

`=1/2 xx 1/(sqrtx)`

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