" (ii) "x^((sin x-cos x))+(x^(2)-1)/(x^(2)+1)

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

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

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

((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))

{ cos (sin ^(-1) x)}^(2) ={sin (cos ^(-1) x)}^(2)

Find the area bounded by the curves y=(sin^(-1)(sin x)+cos^(-1)(cos x)) and y=(sin^(-1)(sin x)+cos^(-1)(cos x))^(2) for 0<=x<=2 pi

(1+sin x+cos x)^(2)=2(1+sin x)(1+cos x)

int(2sin x)/((3+sin2x))dx is equal to (1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(2)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(2sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+c(1)/(4)ln|(2+sin x-cos x)/(2-sin x+cos x)|-(1)/(sqrt(2))tan^(-1)((sin x+cos x)/(sqrt(2)))+cnone of these

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