Question

Qual a Derivada de 3x+1/x

Answer 1

f(x) = 3x + 1/x = 3x + x^-1
f(x)' = 3 + (-1) x^(-2) = 3 - x^(-2)
f(x)' = 3 - 1/x² 

Answer 2

Debe utilizar la siguiente fórmula
                                        $(x^n)'=nx^{n-1}$

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$\left(3x+\dfrac{1}{x}\right)'=(3x)'+\left(\dfrac{1}{x}\right)'\\ \\ \left(3x+\dfrac{1}{x}\right)'=3(x)'+(x^{-1})'\\ \\ \left(3x+\dfrac{1}{x}\right)'=3(1)+(-1)x^{-1-1}\\ \\ \left(3x+\dfrac{1}{x}\right)'=3-x^{-2}\\ \\ \\ \boxed{\boxed{\left(3x+\dfrac{1}{x}\right)'=3-\dfrac{1}{x^2}}}$