Expert: Paul Klarreich - 11/9/2010

Question
Hello, i understand the product rule, and i gather that leibnitz rule is the fundamental explanation for this. However i have a feeling that i have to denote my answers differently compared to when using the product rule. The question i am faced with is- use leibnitz's rule to find d^3/df^3(e^fcosf) even if i used the product rule e.g. u.dv/df +v.du/df i would be confused as i dont fully understand the d^3/df^3 and more precisely the ^3 part. Any help will be greatful!

Answer
Questioner:   jay
Country:  United Kingdom
Category:  Advanced Math
Private:  No
 
Subject:  Leibnitz rule
Question:  Hello, i understand the product rule, and i gather that leibnitz rule is the fundamental explanation for this. However i have a feeling that i have to denote my answers differently compared to when using the product rule. The question i am faced with is- use leibnitz's rule to find d^3/df^3(e^fcosf) even if i used the product rule e.g. u.dv/df +v.du/df i would be confused as i dont fully understand the d^3/df^3 and more precisely the ^3 part. Any help will be greatful!
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I am not sure why you need Leibnitz's rule.  It refers to the derivative of an integral.  You don't seem to have that here.

d^3/df^3(e^fcosf)  simply means the third derivative.

Differentiate e^fcosf, (using the product rule)

Then differentiate the answer, and do it a third time.