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d-dx-ln-x-2-1-x-2-1-




Question Number 68703 by Maclaurin Stickker last updated on 15/Sep/19
(d/dx)(ln((√((x^2 −1)/(x^2 +1)))))=?
ddx(ln(x21x2+1))=?
Commented by MJS last updated on 15/Sep/19
(d/dx)[ln (√((x^2 −1)/(x^2 +1)))]=(1/2)×(d/dx)[ln ((x^2 −1)/(x^2 +1))]=  =(1/2)×((x^2 +1)/(x^2 −1))×((2x(x^2 +1)−2x(x^2 −1))/((x^2 +1)^2 ))=  =((2x)/(x^4 −1))
ddx[lnx21x2+1]=12×ddx[lnx21x2+1]==12×x2+1x21×2x(x2+1)2x(x21)(x2+1)2==2xx41
Commented by Prithwish sen last updated on 15/Sep/19
=(1/( (√((x^2 −1)/(x^2 +1))) )) . (((√(x^2 +1)).((2x)/(2(√(x^2 −1)))) −(√(x^2 −1)).((2x)/(2(√(x^2 +1)))))/(((√(x^2 +1)))^2 ))  =(√((x^2 +1)/(x^2 −1))) .((((x(√(x^2 +1)))/( (√(x^2 −1)))) −((x(√(x^2 −1)))/( (√(x^2 +1)))))/(x^2 +1))  =(√((x^2 +1)/(x^2 −1))).((2x)/( (√(x^2 −1)).(x^2 +1)^(3/2) ))  =((2x)/((x^2 −1)(x^2 +1))) = ((2x)/((x^4 −1)))  pleasecheck.
=1x21x2+1.x2+1.2x2x21x21.2x2x2+1(x2+1)2=x2+1x21.xx2+1x21xx21x2+1x2+1=x2+1x21.2xx21.(x2+1)32=2x(x21)(x2+1)=2x(x41)pleasecheck.
Commented by Maclaurin Stickker last updated on 15/Sep/19
Your answer is right!
Youranswerisright!
Commented by Prithwish sen last updated on 15/Sep/19
Thanks Sir.
ThanksSir.
Commented by mathmax by abdo last updated on 15/Sep/19
let f(x)=ln((√((x^2 −1)/(x^2 +1)))) ⇒f(x)=(1/2){ln(x^2 −1)−ln(x^2 +1)} ⇒  f^′ (x)=(1/2){((2x)/(x^2 −1))−((2x)/(x^2  +1))} =x{(1/(x^2 −1))−(1/(x^2 +1))}  =x{((x^2 +1−x^2 +1)/(x^4 −1))} =((2x)/(x^4 −1))
letf(x)=ln(x21x2+1)f(x)=12{ln(x21)ln(x2+1)}f(x)=12{2xx212xx2+1}=x{1x211x2+1}=x{x2+1x2+1x41}=2xx41

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