differentiate

H(Z)=ln√[(16－Z^2)/(16+Z^2)]
Sol
H(Z)=ln√[(16－Z^2)/(16+Z^2)]
2H(Z)=2ln√[(16－Z^2)/(16+Z^2)]
2H(Z)=ln[(16－Z^2)/(16+Z^2)]
2H(Z)=ln(16－Z^2)-ln(16+Z^2)
2H’(Z)=－2Z/(16－Z^2)－2Z/(16+Z^2)
H’(Z)=-Z/(16－Z^2)－Z/(16+Z^2)
=[－Z(16+Z^2)－Z(16-Z^2)]/(256－Z^4)
=－32Z/(256－Z^4)
=32Z/(Z^4－256)



2013-06-11 11:09:27 補充：
16+Z^2>0

dH(Z)/dZ = d{ ln [ sq. root of ( (16-Z^2) / (16+Z^2) ) ] } /dZ

H ' (Z) = 1/ sq. root of ( (16-Z^2) / (16+Z^2) )
* 1/ [2 * sq. root of ( (16-Z^2) / (16+Z^2) ) ]
* [ (16+Z^2)(-2Z) - (2Z)(16-Z^2) ] / (16+Z^2)^2

H ' (Z) = 1/ [2 * (16-Z^2) / (16+Z^2)]
* [-64Z / (16+Z^2)^2]

H ' (Z) = (16+Z^2) / [2 * (16-Z^2)]
* [-64Z / (16+Z^2)^2]

H ' (Z) = -32Z / [(16+Z^2) * (16-Z^2)]

H ' (Z) = -32Z / (16^2 - Z^4)

H ' (Z) = -32Z / (256 - Z^4)