Differentiate y = (3x − 2)^4

We recognise that this is in the form of a function within a function, i.e u= 3x - 2 is within the u^4 function, therefore here we will use the chan rule to differentiate the equation. 

The chain rule states that dy/dx = dy/du * du/dx.

Here let u = 3x -2, then du/dx = 3. Similarly, y=u^4 so dy/du = 4u^3. Therefore dy/dx = 3 * 4u^3 = 12u^3.

Finally, we substitute u = 3x - 2 into the equation. This therefore gives us, dy/dx = 12(3x - 2)^3.