E^(8x)+e^(-x) find the interval on which f is increasing

Assuming ya mean

take derivitive
remember dy/dx e^x=e^x
also the chain rule

so

find where it equals 0


multiply both sides by e^x

divide both sides by 8

take ln of both sides


divide both sides by 9


x≈-1/5
f'(-1)<0
f'(0)>0

so it is increasing from x to infinity

the interval it is increasing on is