Question

Cálcule a derivada da função:

 

 $</span><var>f(x) = \frac{3}{x} + 2\sqrt{x} - \frac{1}{4\sqrt{x}} </var><span>$

Answer 1

Manipulando a função:
$f(x) = 3 . \frac{1}{x} + 2 x^{ \frac{1}{2} } - \frac{1}{4} . \frac{1}{ \sqrt{x} } \\ f(x)=3 x^{-1} + 2 x^{ \frac{1}{2} } - \frac{1}{4} . \frac{1}{ x^{ \frac{1}{2} } } \\ f(x)= 3 x^{-1} + 2 x^{ \frac{1}{2} } - \frac{1}{4} x^{ -\frac{1}{2} }$
Derivando:
$f'(x)=3.(-1 x^{-2} )+2.( \frac{1}{2}x^{- \frac{1}{2}} )-\frac{1}{4}.(-\frac{1}{2}x^{-\frac{3}{2}})\\ f'(x)= -\frac{3}{x^2} + \frac{1}{\sqrt{x}} + \frac{1}{8 \sqrt{x^3} }}$