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(d)/(dx) {cos ((1-x ^(2))/(1+ x ^(2)))}=...

`(d)/(dx) {cos ((1-x ^(2))/(1+ x ^(2)))}=`

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(d)/(dx) {Cos ^(-1) ""(1-x ^(2))/(1+ x ^(2))}=

d/(dx)[cos(1-x^2)^2]=

d/(dx)[cos(1-x^2)^2]=

d/(dx)(cos^-1((1-x^2)/(1+x^2)))=

(d)/(dx) {Cos ^(-1) ""(x-x ^(-1))/(x + x ^(-1))}=

(d)/(dx)[cos^(-1)sqrt((1+x^(2))/(2))=

(d)/(dx) { sqrt((1- cos x )/( 1+cos x ))}=

d/dx [cos^(-1)((1-x^(2))/(1+x^(2)))] at x = -1/sqrt2 .

(d)/(dx) {Cos ^(-1) ""(sqrt((1 + x)/2))}=