Show how to find the derivative of the cube root of x without using the power rule for differentiation. (i.e. use the four-step process to find f’(x) if f(x) = x1/3.)
We can use the implicit differentiation to find the derivative
==> `y= x^(1/3)`
Cube both sides
==> `y^3 = x`
Now use implicit differentiation.
==> `3y^2 y' = 1`
Now we will divide by `3y^2` .
==> `y'= 1/(3y^2)`
Now we will substitute with `y= x^(1/3)`
`==gt y'= 1/(3(x^(1/3))^2) `
`==gt y'= 1/(3x^(2/3))`