`"If "y=x^(cos)+(cosx)^(x)", prove that "(dy)/(dx)=x^(cosx).{(cosx)/(x)-(sinx)logx}+(cosx)^(x)[(log cos x)-x tan x].`

"If "y=(x)^(cosx)+(sinx)^(tanx)", prove that "(dy)/(dx)=x^(cosx){(cosx)/(x)-(sinx)logx}+(sinx)^(tanx).{1+(log sinx)sec^(2)x}.

"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=(x)^(cosx)+(cosx)^(sinx) , find (dy)/(dx).

If y=e^(sinx)+(tanx)^(x)," prove that "(dy)/(dx)=e^(sinx)cosx+(tanx)^(x)[2x" cosec "2x+log tanx].

Find (dy)/(dx) , when y=x^(cosx)+(cosx)^(sin x)

If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

If y=f(cosx)" and "f'(x)=cos^(-1)x," then "(dy)/(dx)=

int(cos2x)/(cosx-sinx)dx=

If y=(cos x)^((cosx)^((cos x )...oo)) then prove that dy/dx=(y^2 tan x)/(y log (cosx)-1).