If y = `(sinx-xcos x)(cosx +xsin x)`, show that ` dy/dx=x sin2x-x^2 cos 2x`

Find (dy)/(dx) , when If y = (cos x + sinx)/(cos x - sinx) , show that (dy)/(dx) = sec^(2) (x + (pi)/(4)) .

"If "y=(sinx)^(cosx)+(cosx)^(sinx)", prove that "(dy)/(dx)=(sinx)^(cosx).[cot x cos x-sin x(log sinx)]+(cosx)^(sinx).[cosx(log cos x)-sinx tanx].

If y= (sinx -cos x )^((sin x +cos x ) ),then (dy)/(dx)=

If y= (xcos x) ^(x) +(xsin x)^((1)/(x)),then (dy)/(dx) =

If y = (cos x)^((cosx)^((cosx)^(-"to"oo) show that (dy)/(dx) = (cdot y^(2) tan x)/(y log cos x -1) .

If y= (sinx+cosx)+(sin4x+cos4x)^(2) , then :

If sin y=x sin(a+y), then show that: (dy)/(dx)=(sin a)/(1-2x cos a+x^(2))