Calculus/Quotient Rule

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Quotient Rule

Quotient rule

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":

Derivatives of quotients (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