To make life easy, we will break this question up into parts.

Part A:

Find the derivative with respect to x of: y⁴

Part B:

Find the derivative with respect to x of 2x²y²

Now to find the derivative of 2x²y² w.r.t. x we must recognise that it is a product.

If we let u = 2x² and v = y² then we have:

Part C:

Now

and

Now to find for the whole expression:

Working left to right, using our answers from above:

This gives us, on collecting terms:

So we have the required expression: