# How do you differentiate #y=e^x/x^7#?

##### 1 Answer

Jul 30, 2016

#### Explanation:

The easiest way, for me, is to first write this *not* as a quotient:

#y=e^x/x^7=e^x x^-7#

From here, use the product rule, which states that if

So here, we see that

Thus:

#y^'=e^x x^-7+e^x(-7x^-8)#

Simplifying:

#y^'=e^x/x^7-(7e^x)/x^8#

Common denominator:

#y^'=(xe^x-7e^x)/x^8#

#y^'=(e^x(x-7))/x^8#

Note that this can also be done with the quotient rule, which states that if

So, in this case

Thus:

#y^'=(e^x x^7-e^x(7x^6))/(x^7)^2=(e^x x^6(x-7))/x^14=(e^x(x-7))/x^8#