Question

find y for y = 7x^{-2}+2x^{-1}
y = square

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 $y_1 = 7x^{-2}$, using the power - rule: $y_1'=-2\times7x^{-2 - 1}=-14x^{-3}$. For the second term $y_2 = 2x^{-1}$, using the power - rule: $y_2'=-1\times2x^{-1 - 1}=-2x^{-2}$.

Step2: Sum the derivatives of the terms

Since $y = y_1 + y_2$, then $y'=y_1'+y_2'=-14x^{-3}-2x^{-2}$.

Answer:

$-14x^{-3}-2x^{-2}$