Question

4) Resolva está seguinte questão de Funções Derivadas !



g) y= (5/x^2 - √x) (-2x + 3/x)

Answer 1

Resposta:

Explicação passo-a-passo:

$y = \frac{\frac{5}{x^2}+ x^2 -\sqrt{x} }{-2x+\frac{3}{x} }=\frac{\frac{5 +x^4-x^\frac{5}{2} }{x^2} }{\frac{-2x^2+3}{x} }=\frac{5+x^4-x^\frac{5}{2} }{x(-2x^2+3)} = \frac{5+x^4-x^\frac{5}{2} }{3x-2x^3} \\ \\ \\y' = \frac{(5+x^4-x^\frac{5}{2} )'(3x - 2x^3)-(5+x^4-x^\frac{5}{2} )(3x-2x^3)'}{(3x-2x^3)^2} \\ \\ y'=\frac{(4x^3-\frac{5}{2}x^\frac{3}{2})(3x-2x^3)-(5 + x^4-x^\frac{5}{2} )(3-6x^2)}{9x^2-12x^4+4x^6}$

$y'=\frac{12x^4-8x^6-\frac{15}{2}x^\frac{5}{2} +5x^\frac{9}{2} -(15 +3x^4 -3x^\frac{5}{2} -30x^2-6x^6+6x^\frac{7}{2} ) }{9x^2-12x^4+4x^6}\\\\y'=\frac{12x^4-8x^6-\frac{15}{2}x^\frac{5}{2} +5x^\frac{9}{2} -15 -3x^4 +3x^\frac{5}{2} +30x^2+6x^6-6x^\frac{7}{2} }{9x^2-12x^4+4x^6}$