Question

Производная функция
$f(x)=\sqrt[4]{x^{2} }-\frac{3}{\sqrt[3]{x} } +\frac{2}{x^{2} }+\frac{1}{x}+8;f(1)$
решите плз)

Answer 1

$f(x) = \sqrt[4]{ {x}^{2} } - \frac{3}{ \sqrt[3]{x} } + \frac{2}{ {x}^{2} } + \frac{1}{x} + 8 \\ f'(x) = ( \sqrt{x} )' - 3( {x}^{ - \frac{1}{3} } ) + 2( {x}^{ - 2} ) + ( {x}^{ - 1} )' + (8)' = \\ = \frac{1}{2 \sqrt{x} } - 3( - \frac{1}{3} ) {x}^{ - \frac{4}{3} } + 2( - 2) {x}^{ - 3} - {x}^{ - 2} + 0 = \\ = \frac{1}{2 \sqrt{x} } + \frac{1}{ \sqrt[3]{ {x}^{4} } } - \frac{4}{{x}^{3}} - \frac{1}{ {x}^{2} }$