Find the derivative of the function f(x) = x^ | vedclass

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(A) Let $f(x) = x^{3}-27$. By the first principle of derivatives:$f'(x) = \lim_{h 	o 0} \frac{f(x+h) - f(x)}{h}$$f'(x) = \lim_{h 	o 0} \frac{[(x+h)^

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$3x^{2}$

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(A) Let $f(x) = x^{3}-27$. By the first principle of derivatives:$f'(x) = \lim_{h 	o 0} \frac{f(x+h) - f(x)}{h}$$f'(x) = \lim_{h 	o 0} \frac{[(x+h)^{3} - 27] - [x^{3} - 27]}{h}$$f'(x) = \lim_{h 	o 0} \frac{x^{3} + 3x^{2}h + 3xh^{2} + h^{3} - 27 - x^{3} + 27}{h}$$f'(x) = \lim_{h 	o 0} \frac{3x^{2}h + 3xh^{2} + h^{3}}{h}$$f'(x) = \lim_{h 	o 0} (3x^{2} + 3xh + h^{2})$As $h 	o 0$,$f'(x) = 3x^{2} + 3x(0) + (0)^{2} = 3x^{2}$.

Find the derivative of the function $f(x) = x^{3}-27$ using the first principle.

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