y = (5/3) (x - 1)^(3/4) /(x + 2)^5

tomamos logaritmos

ln(y) = ln(5/3) + (3/4) ln(x - 1) - 5 ln(x + 2)

derivamos

y'/y = (3/4) (1/(x - 1)) - 5(1/(x + 2))

y'/y = (3(x + 2) - 5*4 (x - 1))/(4(x - 1)(x + 2))

y'/y = (3 x + 6 - 20 x + 20)/(4(x - 1)(x + 2))

y'/y = (-17 x + 26)/(4(x - 1)(x + 2))

Queda

y'= y * (-17 x + 26)/(4(x - 1)(x + 2))

y'= (5/3) (x - 1)^(3/4) /(x + 2)^5 * (-17 x + 26)/(4(x - 1)(x + 2))

y'= (5/12) (-17 x + 26) (x - 1)^(-1/4) /(x + 2)^6

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Expñicate mejor es sencilla pero no t explicas bien en los exponentes y dividendos