Question

calcule a derivada da função f(x)=3/x² no ponto x=1/2

Answer 1

$f(x) = \frac{3}{x^2}$

reescrevendo a função
$f(x) = 3* x^{-2}$

derivando mantendo a constante 3..e derivando o x^-2
$f'(x) = 3* (-2*x^{-2-1})}\\\\f'(x) = -6x^{-3}\\\\f'(x) = \frac{-6}{x^3}$

no ponto x =1/2
$f'( \frac{1}{2}) = \frac{-6}{ (\frac{1}{2})^3 }= \frac{-6}{ \frac{1}{8} } = \frac{-6*8}{1} =-48\\\\\ \boxed{f'(x) = -48}$

Answer 2

$\huge\mathsf{f(x)=\dfrac{3}{{x}^{2}}}$

$\huge\mathsf{f'(x)=\dfrac{-6}{{x}^{3}}}$

$\huge\mathsf{f'(\dfrac{1}{2})=\dfrac{-6}{{(\frac{1}{2})} ^{3}}}$

$\huge\mathsf{f'(\dfrac{1}{2})=-48}$