`x^(sinx)+(sinx)^(cosx)`

Differentiate the following functions with respect to x : (cos"x")^x (ii) x^(sqrt(x)) (log"x")^(sinx) (iv) (sinx)^(cosx)

Differentiate the following function with respect of x :(sinx+cosx)/(sinx-cosx)

Differentiate the following w.r.t x (sinx-cosx)^(sinx-cosx)

Show that, sin3x + cos3x = (cosx-sinx)(1+4sinx cosx)

Show that, sin3x + cos3x = (cosx-sinx)(1+4sinx cosx)

Differentiate the following w.r.t. x: (sinx-cosx)^(sinx-cosx), pi/4< x <(3pi)/4

Differentiate the following w.r.t. x : (sinx-cosx)^(sinx-cosx),pi/4ltxlt(3pi)/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].

Evaluate: int_0^(pi/2) ((x-pi/4)^2 sinx)/(sinx+cosx)dx