ache os valores absolutos de f(x)=3x/(√4x²-1) no intervalo [1,-1]

Para encontrar a derivada da função dada, devemos realizar os cálculos abaixo:

\(\begin{align} & f=\frac{3x}{\sqrt{4{{x}^{2}}-1}} \\ & f'=3\frac{\frac{2(4{{x}^{2}}-1)-x(\frac{d}{dx}4{{x}^{2}}-1)}{2\sqrt{4{{x}^{2}}-1}}}{4{{x}^{2}}-1} \\ & f'=-\frac{3}{{{\left( 4{{x}^{2}}-1 \right)}^{3/2}}} \\ & f'(1)=-\frac{3}{{{\left( 4\cdot {{1}^{2}}-1 \right)}^{3/2}}} \\ & f'(1)=-\frac{3}{{{\left( 4-1 \right)}^{3/2}}} \\ & f'(1)=-\frac{3}{{{\left( 3 \right)}^{3/2}}} \\ & f'(1)=-\frac{3}{\sqrt{27}} \\ \end{align} \)

\(\boxed{f'\left( 1 \right) = \frac{{ - 3}}{{\sqrt {27} }}}\)

obrigada!!!vlws!