- #1
Orion1
- 973
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Is this the correct symbolic method to differentiate this formula using the limit definition?
[tex]f(x) = x|x|[/tex]
[tex]f'(x) = \lim_{h \rightarrow 0} \frac{(x + h)|(x + h)| - x|x|}{h}[/tex]
[tex]f'(x) = \lim_{h \rightarrow 0} \frac{(x + h)^2 - x^2}{h} = \lim_{h \rightarrow 0} \frac{x^2 + 2hx + h^2 - x^2}{h} = \lim_{h \rightarrow 0} \frac{2hx + h^2}{h} = \lim_{h \rightarrow 0} 2x + h[/tex]
[tex]\boxed{f'(x) = 2|x|}[/tex]
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