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# Find the derivative of the given function from first principle  $x^3-27$

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Let $f(x) = x^3-27$. Accordingly, from the first principle.
$f'(x) = \lim\limits_{h \to 0} \large\frac{f(x+h)-f(x)}{h}$
$= \lim\limits_{h \to 0} \large\frac{[ (x+h)^3-27]-(x^3-27)}{h}$
$= \lim\limits_{h \to 0} \large\frac{x^3+h^3+3x^2h+3xh^2-x^3}{h}$
$= \lim\limits_{h \to 0} \large\frac{h^3+3x^2h+3xh^2}{h}$
$= \lim\limits_{h \to 0} (h^2+3x^2+3xh)$
$= 0+3x^2+0 = 3x^2$
answered Apr 7, 2014