x^(x cos x)+(x^(2)+1)/(x^(2)-1)

If y= x^(sin x- cos x)+ (x^(2)-1)/(x^(2)+1)," find "(dy)/(dx) .

Differentiate x^((sin x-cos x))+(x^(2)-1)/(x^(2)+1) with respect to x:

((1) / ((sec x) ^ (2) - (cos x) ^ (2)) + (1) / ((cos ecx) ^ (2) - (sin x) ^ (2))) ( cos x) ^ (2) (sin x) ^ (2) = (1- (cos x) ^ (2) (sin x) ^ (2)) / (2+ (cos x) ^ (2) (sin x) ^ (2))

2cos^(-1)x=cos^(-1)(2x^(2)-1)

sin{tan^(-1)[(1-x^(2))/(2x)]+cos^(-1)[(1-x^(2))/(1+x^(2))]}=

sin[cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))]=