Differentiate using First Principles y= 5x^-2?

Question

Using first principles, please differentiate y= 5x^-2

Please show your working and answer clearly, 10 points to first correct and clear answer :D thanks in advance

Answer 1

y' = -10 x^-3

Answer 2

y'=lim(h->0) ((5(x+h)^-2-x^-2)/h)=

lim(h->0) ((5(x+h)^-2-x^-2)/h)=

lim(h->0) (5/h)*(1/(x+h)^2-1/x^2)=

lim(h->0) (5/h)*((x^2-(x+h)^2)/(x^2*(x+h)^2))=

lim(h->0) (5/h)*((-2xh-h^2)/(x^4+2x^3h+x^2h^2))=

lim(h->0) (-10x-h)/(x^4+2x^3h+x^2h^2)=

(-10x)/(x^4)=-10x^-3

Answer 3

The power rule says that if y = x^n, then y' = n*x^(n-1).  In this case, y = 5x^(-2), so y' = -10x^(-3) = -10/(x^3).