Question

Determine a derivada da função:

(1 + x - 4√x)/x

Answer 1

Resposta:

$y=\frac{a}{b} \\\\y'=\frac{(a'b)-(ab')}{b^2} \\\\----------------------------------\\\\\\y=\frac{1+x-4\sqrt{x} }{x} =\frac{1+x-4x^{\frac{1}{2} } }{x} \\\\y'=\frac{x.(1-2x^{-\frac{1}{2}})-(1+x-4x^{\frac{1}{2} }).1}{x^2} \\\\y'=\frac{x-2\sqrt{x}-1-x+4\sqrt{x} }{x^2} =\frac{2\sqrt{x}-1 }{x^2}$