Subject: Derivatives, there must be an easier way

The direction read: Take the derivative of each expression.

y = {1+[x+(x² +x³)⁴]⁵}⁶

I tried factoring the whole thing out and then taking the derivative. I think I managed to get the correct answer but I am afraid that the way I did it wasn't the correct way. Is there an easier way to come up with the answer. Could you please show me.

Brad Goorman

I think it is easier to use the chain rule (power rule) than to first multiply. That is:

and continue by applying the chain rule again.