find y for y = 4x^(-2) - 2x^(-1). y = □

Explanation:

Step1: Recall power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y'=nax^{n - 1}$.

Step2: Differentiate $4x^{-2}$

For $y_1 = 4x^{-2}$, using the power - rule with $a = 4$ and $n=-2$, we have $y_1'=-2\times4x^{-2 - 1}=-8x^{-3}$.

Step3: Differentiate $-2x^{-1}$

For $y_2=-2x^{-1}$, using the power - rule with $a = - 2$ and $n=-1$, we get $y_2'=-1\times(-2)x^{-1 - 1}=2x^{-2}$.

Step4: Find $y'$

Since $y = y_1 + y_2$, then $y'=y_1'+y_2'=-8x^{-3}+2x^{-2}$.

Answer:

$-8x^{-3}+2x^{-2}$