Resposta :
[tex]\boxed{f(x)= x^{2} } \\
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f'(x)= \lim_{\Delta x \to 0} \frac{f(x+ \Delta x)-f(x)}{\Delta x} \\
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f'(x)=\lim_{\Delta x \to 0} \frac{f(x+ \Delta x)^2-x^2}{\Delta x} \\
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f'(x)=\lim_{\Delta x \to 0} \frac{x^2+2x \Deltax+ (\Delta x)^2-x^2}{\Delta x} \\
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f'(x)=\lim_{\Delta x \to 0} \frac{2x \Deltax+ (\Delta x)^2}{\Delta x} \\
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f'(x)=\lim_{\Delta x \to 0} (2x \Deltax+ \Delta x) \\
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\boxed{f'(x)=2x } \\
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\boxed{f'(1)=2.1=2}[/tex]