Find the derivatives of the following function from first principle: `x^3-27`

Explanation

We have given the function `x^3-27`

Then let, `f(x)= x^3-27`

Hence, `f(x+h)= (x+h)^3-27`

`f(x+h)=x^3+h^3+3x^2h+3xh^2-27`

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

`f'(x)=(lim)_(h->0)((x^3+h^3+3x^2h+3xh^2-27)-(x^3-27))/h`

`f'(x)=(lim)_(h->0)(x^3+h^3+3x^2h+3xh^2-27-x^3+27)/h`

`f'(x)=(lim)_(h->0)(h^3+3x^2h+3xh^2)/h`

...