The derivative of f(x)*g(x)/h(x)

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SUMMARY

The derivative of the function f(x)*g(x)/h(x) can be calculated using the quotient rule, treating f(x)*g(x) as a single function v(x). The derivative is expressed as [(fg)'h - fgh']/h², which simplifies to [f'gh + fg'h - fgh']/h². This method requires applying the product rule to differentiate v(x). The discussion confirms the correct application of these rules, emphasizing the importance of sign accuracy in differentiation.

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What is the derivative rule for a function times another function divided by another function?
 
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Just treat f(x)*g(x) as one function, say v(x). So you have the derivative of {{v(x)} \over {h(x)}} which you differentiate like normal. When you differentiate v(x), you'll simply have a product rule to deal with.
 
It is easiest to do in two steps:
[(fg)'h - fgh']/h2 = [f'gh + fg'h - fgh']/h2
 
Thank you, I was trying to verify if that worked by doing it both ways. I figured out my problem. I had the signs on the v(x)/h(x) derivative rule switched.
 

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