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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
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)
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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