MR=P[1 – (1/εP)] or MR = P[1 + (1/εP)]?

Got stucked on this equation. I know MR=Δ_TR/ΔQd, while εP=–(% change in QD_) ÷ (% change in P)=-_ΔQd/_ΔP.

According to the formula, MR=P-P/εP=P-P*(-_ΔQd/__ΔP)=P+P*__ΔP/_ΔQd.

_Δ_TR/_ΔQd= P+P* ΔP/_ΔQd

_So Δ_TR=P*_ΔQd+P*__ΔP=P(__ΔQd+_ΔP)?

Can’t get any further. Also I have seen another equation on internet: MR = P[1 + (1/εP)], which is different with the one titled.

Could someone please explain it for me? Thanks!

here P express the old price not the new one in the formula TR = P Δ Q +Q Δ P so forget about this derivation. Now take it this way:

P = f(Q) εP = - Q/Δ P)*(P/Q) ------> dP/dQ =- P/(Q* εP ) the negative sign express the demand sloping downward MR = Δ TR/ Δ Q by definition so it is derivative of TR with respect to Δ Q when Δ Q is too small

TR = PQ so MR= Δ TR/ Δ Q = dTR/dQ = (dP/dQ)Q + (dQ/dQ)P basic calculus

MR = P -QP/(Q*εP) = P(1-1/εP)