Differentiate the following functions with respect to x :

sin (x^x)

Let y = sin (x^x)

Take sin inverse both sides:

⇒ sin^-1 y = sin^-1 (sin x^x)

⇒ sin^-1 y = x^x

Taking log both the sides:

⇒ log (sin^-1 y) = log x^x

⇒ log (sin^-1 y) = x log x {log x^a = alog x}

Differentiating with respect to x:

Put sin (x^x) :

{sin² x + cos² x=1}