find an expression for d^2P/dτ^2 by implicit differentiating f'(P+τ) ((dP/dτ)+1) = g'(P)(dP/dτ) w.r.t. τ

RyanKooper

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The question: find an expression for d^2P/dτ^2 by implicit differentiating f'(P+τ) ((dP/dτ)+1) = g'(P)(dP/dτ) w.r.t. τ . P'=f'/(g'-f')

What I get is: f''(p'+1)^2 +f'p''=g''(p')^2 +g'P'' but when I try solving for P'' after substituting P' for f'/(g'-f') i cant get it right.

The answer is supposed to be P''=[f''(g')^2 - g''(f')^2]/(g'-f')^3
 
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