Find the derivatives of the following function from first principle: `1/(x^2)`

Explanation

We have given the function `1/(x^2)`
Then let, `f(x)=1/(x^2)`

Hence, `f(x+h)=1/((x+h)^2)`

`f(x+h)=1/(x^2+h^2+2xh)`

Therefore, `f'(x)=(lim)_(h->0)(f(x+h)-f(x))/h`

`f'(x)=(lim)_(h->0)((1/(x^2+h^2+2xh))-(1/(x^2)))/h`

`f'(x)=(lim)_(h->0)((x^2-x^2-h^2-2xh)/(x^2(x^2+h^2+2xh)))/h`

`f'(x)=(lim)_(h->0)(-h^2-2xh)/(hx^2(x^2+h^2+2xh))`

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