how to differentiate this problem?

[tex]3 \sqrt{x + \frac{2}{x {}^{2} } } - x \\ \\ [/tex]
the sqrt above is only over the x

the answer was

[tex] \frac{1}{3} x { \frac{ - 2}{3} }^{} - 4x {}^{ - 3} -1[/tex]
but how? could someone pls explain step by step on how to receive this f'(x)?

thank you for your help

Respuesta :

first  change the radical to exponents= and note that 2 / x^2 =  2x^-2:-

y = 3x^-1/2 + 2x^-2 - x

dy/dx  = 3/2 * x -3/2  + 2*-2 x^-3 - 1

 =  3/2 x^-3/2 - 4x^-3 - 1