Question

Richard Feynman, the great 20th century physicist, used the following rule for differentiati of a product of powers: Given f = k·v.vb... (where k, a, b,... are constants), df dr du/dx fa dv/dk +6 + u a) Derive Feynman's rule using logarithmic differentiation. (23 - 22) b) Compute the derivative of f(x) = 6 You don't need to simplify your ans Vx+ 5x2

please explain all steps in detail

Answer 1

Soll (9) f = x. 49. vb both sides, Take In luffy In (K. u. vb ..... ) T = Inffy - In(k) + Inu" + 14 Cub) + ㅋ In(f) - 다. lu(k) + a ln(4) + b In(v) + sides worot 기 Differentiating both d luct dink b dln(w) + dx so, il + 9 d lucy + - -- AX Әх =) = + a. I. du + 2.1 dv + u dx v ax So, df + + - dx u (6) f = Take Sides, √x+502 I. df f dx q. dy b dv dx v dx Aug 6 (23-12) ² Ja + 5x² In both fluoralna) luct) In 6 (2²-x22 & lucht lu(6[a?<»%) - In (atske Inff) 2 1n (6 (23-12) +(+5) Differentiating both Sides I df 2. 1 X6 (32?=2x) x (1 +102) f dx 6 (2²x) 2 (a+50²) df f (2 20312-20) dx (23-22) 2(2+522) 6 (32-22)? ( 2 (322—20) Ja +502 1x 2-14 2(9+532) = 7) Worot a So, +104 So, 1 + 10% - Ang