Question

Preciso do processo não do da resposta
Derivada:
$F(x)= \sqrt{x} ( \frac{x}{3} -4)$

Answer 1

Olá Joyce

$f(x)= \sqrt{x} ( \frac{x}{3} -4) \\ multiplicando\ (\sqrt{x})\ temos. \\ \\ f(x)= \frac{x \sqrt{x} }{3} -4 \sqrt{x} --\ \textgreater \ sabe-se\ que\ [ \sqrt{x} = x^{1/2} ] \\ \\ f(x)= \frac{x. x^{1/2} }{3} -4 x^{1/2} \\ \\ f(x)= \frac{ x^{3/2} }{3} -4 x^{1/2} \\ \\ derivando\ temos.$

$f'(x)= \frac{( x^{3/2})'.3- x^{3/2} .(3)' }{ 3^{2} } -4. \frac{1}{2} . x^{-1/2} \\ \\ f'(x)= \frac{ \frac{3}{2}. x^{1/2} .3- x^{3/2}.0 }{9} -2 x^{-1/2} \\ \\ f'(x)= \frac{ \frac{9}{2} x^{1/2} -0 }{9} - \frac{2}{ \sqrt{x} } \\ \\ f'(x)= \frac{ \frac{\not9}{2} \sqrt{x} }{\not9} - \frac{2}{ \sqrt{x} } \\ \\ f'(x)= \frac{ \sqrt{x} }{2} - \frac{2}{ \sqrt{x} } \\ \\\boxed{\boxed{ f'(x)= \frac{x-4}{2 \sqrt{x} }} }$

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                                        Espero ter ajudado!!