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Question
k xn
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Solution
\[\frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{k \left( x + h \right)^n - k x^n}{h}\]
\[ = \lim_\left( x + h \right) - x \to 0 \frac{k \left[ \left( x + h \right)^n - x^n \right]}{\left( x + h \right) - x}\]
\[\text{ Here, we have }:\]
\[ \lim_{x \to a} \frac{x^m - a^m}{x - a}=m a^{m - 1} \]
\[ = k n x^{n - 1}\]
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