The answer I got is dw/dt = -4sin8xsin4y + 4cos8xcos4y * 5t^4

It says that the answer is right but in order to get credit, it has to be answered in terms of the independent variable.

The problem is: Use the chain rule to find dw/dt, where w=cos8xsin4y, x=t/2 and y=t^5.How would I write my answer so that it will express the answer in terms of the independent variable?

In your answer, replace x by t/2 and y by t^5. Then your answer is a function of t, the independent variable.

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