- Edited
You use product rule when you want to differentiating values that are being multiplied (hence it is named product).
For example: To find the derivative of 2xe3x you use product rule.
= (2)(e3x) + (2x)(3e3x) = 2e3x + 6xe3x
You use quotient rule when you want to differentiating values that are being divided (hence it is named quotient).
For example: To find the derivative of 2x/e3x you use quotient rule.
= (2)(e3x) - (2x)(3e3x)/(e3x)2