Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
We need to prove where t and and be V Dv (tg) = f Dv g + gDvf д I are continuously differentiable function a unit vector in R² c is constant

We need to prove where t and and be V Dv (tg) = f Dv g + gDvf д I are continuously differentiable function a unit vector in R² c is constant

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
100%

TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

This is the solution but I don't quite understand what it says in the writing, I need this to be made easier for me by writing it in digital format

We need to prove: Dv (tg) = f Dvg+ gDvf where I and I are continuously differentiable function g and V be a unit vector in R² c is constant Proof: Dv (tg) = lim fg (((y) +hi) - fg(x, y) nyo h lim tray) thì) ที่ adding and substracting fex,y) g[(x,y) thú}, g(x,y) = + [(y)+ hu], g(xi) fr1.y), weget Now, after this, = = = arrany = lim t 40 ho h li'm ± [f[wy) + hv].g[(x,y)thv] -f(x,y). gltiy) + fexy). g [(y) thi] + g(x₁y); f [(x₁y) +hv] + g(xy). feliy) - fravy) g [(x,y) thi]-gexy) [fex,y) thr] - geziy) -fexix)] _g[(x,y) th√ ] - fexias g11.2)] the terms, we [fexiy) [g(x,y)+hiv]_gex,y)] + gexry) [fellysthu)- texs)]/ +g [[xy) th√) [fxy) th√ - Jexy)) + get genvy) [f([^vy) thú) - Jers) ] - fexiy) Drgexy)+ делін) От texiy) Dv (g) = fDvg+ govt
Transcribed Image Text:We need to prove: Dv (tg) = f Dvg+ gDvf where I and I are continuously differentiable function g and V be a unit vector in R² c is constant Proof: Dv (tg) = lim fg (((y) +hi) - fg(x, y) nyo h lim tray) thì) ที่ adding and substracting fex,y) g[(x,y) thú}, g(x,y) = + [(y)+ hu], g(xi) fr1.y), weget Now, after this, = = = arrany = lim t 40 ho h li'm ± [f[wy) + hv].g[(x,y)thv] -f(x,y). gltiy) + fexy). g [(y) thi] + g(x₁y); f [(x₁y) +hv] + g(xy). feliy) - fravy) g [(x,y) thi]-gexy) [fex,y) thr] - geziy) -fexix)] _g[(x,y) th√ ] - fexias g11.2)] the terms, we [fexiy) [g(x,y)+hiv]_gex,y)] + gexry) [fellysthu)- texs)]/ +g [[xy) th√) [fxy) th√ - Jexy)) + get genvy) [f([^vy) thú) - Jers) ] - fexiy) Drgexy)+ делін) От texiy) Dv (g) = fDvg+ govt
Expert Solution
steps

Step by step

Solved in 3 steps with 2 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