Differentiate the following function

y = e^x^5-7x-8

the answer is e^x^5-7x-8(5x^4-7), but Id like to know how to work it out.

The way you typed it, I see it as

y = e^(x^5) - 7x - 8

If that is the way it is, then its derivative is
(5x^4)(e^(x^5) - 7