Differentiate the following function with respect to `x` from first principle: `sqrt(4-x)`

Explanation

We have given the function `sqrt(4-x)`
Then let, `f(x)=sqrt(4-x)`

Hence, `f(x+h)=sqrt(4-(x+h))`

Therefore, `f'(x)=(lim)_(h->0)(f(x+h)-f(x))/h`

`f'(x)=(lim)_(h->0)(sqrt(4-(x+h))-sqrt(4-x))/h`

`f'(x)=(lim)_(h->0)((sqrt(4-(x+h))-sqrt(4-x))(sqrt(4-(x+h))+sqrt(4-x)))/(h(sqrt(4-(x+h))+sqrt(4-x))`

`f'(x)=(lim)_(h->0)(4-(x+h)-(4-x))/(h(sqrt(4-(x+h))+sqrt(4-x))`

`f'(x)=(lim)_(h->0)(4-x-h-4+x)/(h(sqrt(4-(x+h))+sqrt(4-x))`

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