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

1.	Find the derivative of `sqrt(4-x)`w.r.t. `x`using the first principle.
Answer» Correct Answer - `(-1)/(2sqrt(4-x))` `"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))`

Discussion

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