Derive a função usando a regra do quociente.... Pergunta de ideia deEriivan

May 2020 1 269 Report

Derive a função usando a regra do quociente

$\boxed{f(x)= \frac{x^2-a^2}{x^2+a^2}}$

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A regra do quociente é:

$\boxed{\left(\frac{f}{g}\right)'=\frac{gf'-fg'}{g^2}}\\
\\
f(x)=x^2-a^2\\
\\
f'(x)=2x\\
\\
g(x)=x^2+a^2\\
\\
g'(x)=2x\\
\\
g^2(x)=(x^2+a^2)^2\\
\\
Substituindo: \\
\\
$

$\boxed{f'(x)=\frac{(x^2+a^2).2x-(x^2-a^2).2x}{(x^2+a^2)^2}=\frac{4a^2x}{(x^2+a^2)^2}}$

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Eriivan Obrigado MATHSPHIS.

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