Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Exercise 4.3.2. Let I CR be an open interval, let c E I, let n E N and let f1,..., fn : I¬R be functions. Suppose that fi is differentiable at c for all i e {1,...,n}. Prove that fif2 fn is differentiable at c, and find (and prove) a formula for (fi f2 -… fn)'(c) in terms of fi(c), ... fn(c) and f{(c),...f,(c). ...

Exercise 4.3.2. Let I CR be an open interval, let c E I, let n E N and let f1,..., fn : I¬R be functions. Suppose that fi is differentiable at c for all i e {1,...,n}. Prove that fif2 fn is differentiable at c, and find (and prove) a formula for (fi f2 -… fn)'(c) in terms of fi(c), ... fn(c) and f{(c),...f,(c). ...

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

4.3.2

Please include a formal proof. 

Exercise 4.3.2. Let I CR be an open interval, let c E I, let n E N and let fi,..., fn : I–R be functions. Suppose that fi is differentiable at c for all i E {1,...,n}. Prove that fi f2 -. fn is differentiable at c, and find (and prove) a formula for (fi f2·… fn)' (c) in terms of fi (c), ..., fn(c) and f{(c),..., f„(c).
Transcribed Image Text:Exercise 4.3.2. Let I CR be an open interval, let c E I, let n E N and let fi,..., fn : I–R be functions. Suppose that fi is differentiable at c for all i E {1,...,n}. Prove that fi f2 -. fn is differentiable at c, and find (and prove) a formula for (fi f2·… fn)' (c) in terms of fi (c), ..., fn(c) and f{(c),..., f„(c).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS