use-the-first-principle-to-find-value-of-f-x-x-1-3-

Question Number 22105 by j.masanja06@gmail.com last updated on 11/Oct/17

u s e t h e f i r s t p r i n c i p l e t o f i n d

v a l u e o f

f (x) = {(x)}^{\frac{1}{3}}

Answered by $@ty@m last updated on 11/Oct/17

\frac{d y}{d x} = \lim_{δ x \to 0} \frac{f (x + δ x) - f (x)}{δ x}

= \lim_{x + δ x \to x} \frac{{(x + δ x)}^{\frac{1}{3}} - x^{\frac{1}{3}}}{(x + δ x) - x}

= \frac{1}{3} x^{\frac{1}{3} - 1}, u s i n g f o r m u l a \lim_{x \to a} \frac{x^{n} - a^{n}}{x - a} = {n a}^{n - 1}

= \frac{1}{3 x^{\frac{2}{3}}} A n s .

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