DERIVATIVE OF CUBE ROOT OF X BY FIRST PRINCIPLE

Formula to find derivative of a function f(x) by first principle :

This is also called as limit definition of the derivative.

To get rid of the cube root in ³√(x + h) - ³√x, we have to use the following algebraic identity.

a³ - b³ = (a - b)(a² + ab + b²)

If a = ³√(x + h) and b = ³√x, we have

Multiply both numerator and denominator by

Use the following algebraic identity in numerator part.

a³ - b³ = (a - b)(a² + ab + b²)