There rule similar to the product rule for quotients. To prove it, we go to the definition of the derivative:
This leads us to the so-called "quotient rule":
Which some people remember with the mnemonic "low D-high minus high D-low (over) square the low and away we go!"
The derivative of is:
Remember: the derivative of a product/quotient is not the product/quotient of the derivatives. (That is, differentiation does not distribute over multiplication or division.) However one can distribute before taking the derivative. That is