19.5. Prove the following identities for differentiation by finding the real and imaginary parts of the function-u(x, y) and v(x,y)–and differentiat- ing them: dg (b) =Ư9) = +f df (fg) dz dg (a) dz df (f +g) = dz dz dz dz d. (c) f'(2)g(z) = g'(z)f (z) [g(2)]² where g(z) # 0. dz
19.5. Prove the following identities for differentiation by finding the real and imaginary parts of the function-u(x, y) and v(x,y)–and differentiat- ing them: dg (b) =Ư9) = +f df (fg) dz dg (a) dz df (f +g) = dz dz dz dz d. (c) f'(2)g(z) = g'(z)f (z) [g(2)]² where g(z) # 0. dz
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![19.5. Prove the following identities for differentiation by finding the real
and imaginary parts of the functionu(r, y) and v(x, y)-and differentiat-
ing them:
df
dg
df
dz
f'(z)g(z) – g'(z)f(z)
g(2)]2
(a) 부(+9)=a
dg
(b) 는(f9)=D9+ f군
g+f.
dz
dz
dz
dz
(c)
where g(z) # 0.
(6)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2db0f564-5560-48e1-ad37-7a23e30509ae%2F91190ccf-99c4-4c70-bb67-6dcd63147b33%2Fqgb3lxa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:19.5. Prove the following identities for differentiation by finding the real
and imaginary parts of the functionu(r, y) and v(x, y)-and differentiat-
ing them:
df
dg
df
dz
f'(z)g(z) – g'(z)f(z)
g(2)]2
(a) 부(+9)=a
dg
(b) 는(f9)=D9+ f군
g+f.
dz
dz
dz
dz
(c)
where g(z) # 0.
(6)
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