Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Quotient and Product rule confirmation?
Considering that a function
f(x) = g(x)/h(x)
can be thought of as:
f(x) = g(x) * 1/h(x)
Is it possible to treat a quotient of functions as just a product of functions as shown, and just differentiate from there? I have tried this and it works, but i just wanted to be sure.
Also, if this is a viable option (because i always forget the quotient rule formula) will it still work in all cases, such as when there is a restricted domain or it is a hybrid function?
Thanks your your help in advance.
5 Answers
- ?Lv 71 decade agoFavorite Answer
It does indeed!
The quotient rule says that f' = (hg' − gh')/h²
Let k(x) = 1/h(x) = [h(x)]^(−1)
By the product rule, f' = kg' + gk'
By the chain rule, k' = (−1)h^(−2)h' = −h'/h², then
f' = kg' + gk' = g'/h − gh'/h² = hg'/h² − gh'/h² = (hg' − gh')/h²,
in agreement with the quotient rule.
- jilekLv 45 years ago
it is going to count cuz think of approximately what occurs if u opposite the order of this -3-3 u get 3-(-3) your order adjustments that could substitute it from a destructive to helpful. in the quotient rule it could cahnge plenty greater thinking the backside bein squared and what no longer
- Fazaldin ALv 71 decade ago
The quotient rule is :
f' = (hg' − gh')/h²
Let k(x) = 1/h(x) = [h(x)]^(−1)
And By the product rule, f' = kg' + gk'
Also
By the chain rule, k' = (−1)h^(−2)h' = −h'/h²,
Then
f' = kg' + gk' = g'/h − gh'/h² = hg'/h² − gh'/h² = (hg' − gh')/h²,
Hence : Q . E . D.
