find the derivative of the function. y = 11x^2 - 9x - 9x^(-2) dy/dx = □

Explanation:

Step1: Apply power - rule to each term

The power - rule for differentiation is $\frac{d}{dx}(ax^n)=nax^{n - 1}$. For the first term $11x^2$: $\frac{d}{dx}(11x^2)=2\times11x^{2 - 1}=22x$. For the second term $-9x$: $\frac{d}{dx}(-9x)=-9\times1x^{1 - 1}=-9$. For the third term $-9x^{-2}$: $\frac{d}{dx}(-9x^{-2})=-2\times(-9)x^{-2 - 1}=18x^{-3}$.

Step2: Combine the derivatives of each term

$\frac{dy}{dx}=\frac{d}{dx}(11x^2)+\frac{d}{dx}(-9x)+\frac{d}{dx}(-9x^{-2})$. So, $\frac{dy}{dx}=22x-9 + 18x^{-3}$.

Answer:

$22x-9+\frac{18}{x^{3}}$