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derivative of f(x)=√(x^2+4x) using the formal definition of a derivative?
formal def of a derivative: (f(x+h)-f(x))/h
1 Answer
- EMLv 78 years agoFavorite Answer
lim {sqrt[(x + h)² + 4(x + h)] - sqrt[x² + 4x]} / h =
h->0
lim {sqrt[(x + h)² + 4(x + h)] - sqrt[x² + 4x]}{sqrt[(x + h)² + 4(x + h)] + sqrt[x² + 4x]} / (h{sqrt[(x + h)² + 4(x + h)] + sqrt[x² + 4x]}) =
h->0
lim {[(x + h)² + 4(x + h)] - [x² + 4x]} / (h{sqrt[(x + h)² + 4(x + h)] + sqrt[x² + 4x]}) =
h->0
lim {x² + 2xh + h² + 4x + 4h - x² - 4x} / (h{sqrt[(x + h)² + 4(x + h)] + sqrt[x² + 4x]}) =
h->0
lim {2xh + h² + 4h} / (h{sqrt[(x + h)² + 4(x + h)] + sqrt[x² + 4x]}) =
h->0
lim {2x + h + 4} / {sqrt[(x + h)² + 4(x + h)] + sqrt[x² + 4x]} =
h->0
(2x + 4) / {2sqrt[x² + 4x]} =
(x + 2) / sqrt[x² + 4x]
