Question

How do you find the derivative of `y=root3(5x^3 -3x^2 +6)`?

Answer 1

`dy/dx=(15x^2-6x)/(3root(3)((5x^3-3x^2+6)^2)`

Explanation:

Using laws of indices and surds we may write this function as

`y=(5x^3-3x^2+6)^(1/3)`

Now we may use the power rule to differentiate it as follows :

`dy/dx=1/3(5x^3-3x^2+6)^(-2/3)*(15x^2-6x)`

`=(15x^2-6x)/(3root(3)((5x^3-3x^2+6)^2)`