To find the derivative of the function y = rac{1}{x^2} imes x^n at x = 1, we first simplify the function and then differentiate it.
First, we can rewrite the function as:
y = x^{n-2}
Now, we can differentiate this with respect to x. Using the power rule of differentiation:
rac{dy}{dx} = (n-2)x^{(n-2)-1} = (n-2)x^{n-3}
Next, we evaluate the derivative at x = 1:
rac{dy}{dx} igg|_{x=1} = (n-2) imes 1^{n-3} = n-2
Thus, the derivative of y at x = 1 is:
n – 2