can someone help me calculate g'(a) for g(x) = x^(2/3) using g'(a) = lim h-->0 [(x+h)^(2/3)-x^(2/3)]/h ? Thanks for the help!
recommend using the alternate definition ...
$\displaystyle \displaystyle g'(a) = \lim_{x \to a} \frac{g(x) - g(a)}{x - a}
$
$\displaystyle \displaystyle g'(a) = \lim_{x \to a} \frac{x^{2/3} - a^{2/3}}{x - a}$
$\displaystyle \displaystyle g'(a) = \lim_{x \to a} \frac{(x^{1/3} - a^{1/3})(x^{1/3} + a^{1/3})}{(x^{1/3} - a^{1/3})(x^{2/3} + a^{1/3}x^{1/3} + a^{2/3})}$
$\displaystyle \displaystyle g'(a) = \lim_{x \to a} \frac{x^{1/3} + a^{1/3}}{x^{2/3} + a^{1/3}x^{1/3} + a^{2/3}} = \frac{2}{3a^{1/3}}$