Downey is licensed under a Creative Commons Attribution 3.0 License. Feel free to enter your own functions for f and g, to explore what the product and quotients, and their derivatives, look like.If you call the function on top HI and the one on the bottom HO, and their derivatives dHI and dHO, then the rule becomes, which can be read as "HO dHI minus HI dHO, all over HO HO." This is sometimes referred to as the HIdHO rule (think Cab Calloway singing Hi De Ho, dressed up as Santa Claus.). I learned a mneumonic to help remember this formula. Select the third example, showing a quotient.In other words, the derivative of a product of two functions equals the derivative of the first times the second, plus the first times the derivative of the second. Clearly the derivative of h is not just the product of the derivatives of f and g (if it was, it would look like a stretched cosine). Here, f and g are the same, but h is now the product. The product rule gives gives V(0) 1·(1)+2♱.
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