Will the cost of detergents rise as the cost of crude oil rises?

This seems a certainty. Detergents are chemical surfactant petrochemicals derived from crude oil. The basic surfactant building blocks, with one exception, are all derived from crude oil. Unless detergent companies choose to lower their profit margins to keep the cost of detergent low, you will pay more and more for detergent, just as you pay more and more to fuel your car. As the raw material cost of detergent increases, so do the detergent costs for end-users. Moreover, their plastic containers (which are made of only 25% recycled plastic) are made of petrochemicals and shipping these bulky and heavy bottles costs more because of record high fuel prices. These extra costs are also ultimately paid by the end user.