A curve has equation `y = 2x^3 - 6x^{4/3} - x^{-1}`. (a) Find `dy/dx`. (b) Find the exact value of `dy/dx` at `x=3`.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. M1 for attempt to differentiate `x^n` to `nx^(n-1)`. (Allow one error) OR for differentiating `2x^3` to `6x^2` and `-6x^(4/3)` to `-8x^(1/3)` or `-x^(-1)` to `+x^(-2)` (any non zero A)
2. A1 for `6x^2 - 8x^(1/3) + x^(-2)` or `6x^2 - 8x^(1/3) + 1/x^2` (All terms correct and simplified).
3. B1 for substituting `x=3` into their `dy/dx`. (Must be an attempt to differentiate)
4. M1 for correct powers for `3^(1/3)` and `3^(-2)` OR for `3^(1/3)` and `1/3^2`.
5. A1 for `54 - 8³√3 + 1/9` or `54 + 1/9 - 8³√3` (o.e. e.g. `487/9 - 8³√3`)