Find the derivative of `sqrt(4-x)` w.r.t. `x` using the first principle.

Answer

`(-1)/(2sqrt(4-x))`

Explanation

`"Let "f(x)=sqrt(4-x)." Then "f(x+h)=sqrt(4-(x+h))." Therefore,"`
`(d)/(dx)(f(x))=underset(hrarr0)lim(f(x+h)-f(x))/(h)`
`=underset(hrarr0)lim(sqrt(4-(x+h))-sqrt(4-x))/(h)`
`=underset(hrarr0)lim({sqrt(4-(x+h))-sqrt(4-x)}{sqrt(4-(x+h))+sqrt(4-x)})/(h{sqrt(4-(x+h))+sqrt(4-x)})`
`=underset(hrarr0)lim(4-(x+h)-(4-x))/(h{sqrt(4-(x+h))+sqrt(4-x)})`
`=underset(hrarr0)lim(-h)/(h{sqrt(4-x-h)+sqrt(4-x)})=(-1)/(2sqrt(4-x))`