let y = (sin x)^{cos x} + (cos x)^{sin x}

⇒ y = a + b

where a= (sin x)^{cos x}; b = (cos x)^{sin x}

a= (sin x)^{cos x}

Taking log both the sides:

⇒ log a= log (sin x)^{cos x}

⇒ log a= cos x log (sin x)

{log x^a = alog x}

Differentiating with respect to x:

b = (cos x)^{sin x}

Taking log both the sides:

⇒ log b= log (cos x)^{sin x}

⇒ log b= sin x log (cos x)

{log x^a = alog x}

Differentiating with respect to x: