find y for y = 6x^(-5) - 7x^(-1)\ny = □

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y'=nax^{n - 1}$. For the first term $y_1 = 6x^{-5}$, using the power - rule: $y_1'=-5\times6x^{-5 - 1}=-30x^{-6}$. For the second term $y_2=-7x^{-1}$, using the power - rule: $y_2'=-1\times(-7)x^{-1 - 1}=7x^{-2}$.

Step2: Combine the derivatives of the terms

Since $y = y_1 + y_2$, then $y'=y_1'+y_2'$. So $y'=-30x^{-6}+7x^{-2}$.

Answer:

$-30x^{-6}+7x^{-2}$