Question

differentiation form first principles y=1/x^2

Answer 1

form or from first principles?

The derivative of y = x^-2 is
dy/dx = -2 x^-3

For a 'first principles' derivation, you will have to use the definition of the derivative and calculate some limits.

I recommend that you perform that exercise yourself.

dy/dx = lim (1/d)[1/(x+d)^2 - 1/d^2]
.......d -> 0

Answer 2

i get so far then i get stuck i think im doing something wrong

f(x+h)-f(x) = 1/(x+h)^2 - 1/x^2
= x^2 - x^2 -2xh -h^2 above divided by(x^2+2xh+h^2)(x^2)
= -2xh -h^2/x^4+2x^3h+h^2x^2

then i know i need to divide by h but i cant seem to get to what i want