Drainville - Dishsoap/ detergent's effect on plants varies with the mode of exposure. Dawn, Palmolive, Joy, ...... dishsoap, as an example, are each and all a mishmash of chemicals, at least eleven of which are phytotoxic. If the top of the plant is sprayed thoroughly with even mild detergent solutions such that all surfaces including leaves are covered, the detergent can easily dissolve the protective coating of cuticular wax on the leaves of the plant, causing abnormally high rates of water loss and possible necrosis of all or part of the leaf. Cuticular waxes prevent leaves from drying out, and help stop pathogens from attacking the leaf. Strong solutions will even dissolve cell membranes, causing death of the cells.
If a detergent solution is used as a soil drench or makes its way into the soil as a consequence of over-spray or run-off, the effect on roots is immediate. Because one of the main function of roots is to absorb water and nutrients dissolved in water, they lack the waxy protective coating that leaves employ. Detergent solution in contact with root cells can quickly dissolve the lipid membrane surrounding cells, killing the cells and inhibiting water/ nutrient uptake. Hair cells growing as appendages off larger roots do the lion's share of assimilating water and nutrients, and these very delicate cells would be the first casualty of any detergent in the root zone.
There are widely available insecticidal soaps, designed to be used topically and made mixing potassium with only long chain fatty acids, carefully selected and specifically formulated to be safe for mammals & birds, death on most insects they contact, and most important, safe for plants. If you need something "soapy", it would be much better if you selected a product intended for use on plants than one intended for other purposes.
If you don't wish to purchase insecticidal soap, you'd be better served to spritz at 4 day intervals with a 3:1 solution of water:70% isopropyl/rubbing alcohol - not the wintergreen scented product. As with the insecticidal soap, the alcohol solution depends on contact, so be sure to spray all parts of the plant thoroughly and cover the soil until the application has dried.
Al