Question

How do you differentiate `y = (sqrt x + (1/2))(x^3 + x^(1/3))`?

Answer 1

`dy/dx = (7x^(5/2) + 3x^2)/2 + (5x^4 + x^(-2/3))/6`

Explanation:

The easiest way is to foil and then derivate

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

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

`y = x^(7/2) + x^3/2 + x^(5/6) + x^(1/3)/2`

`dy/dx = (7x^(5/2))/2 + (3x^2)/2 + (5x^4)/6 + (x^(-2/3))/6`

`dy/dx = (7x^(5/2) + 3x^2)/2 + (5x^4 + x^(-2/3))/6`