Differentiate (x.cos x)^x + (x.sin x)^1/x with respect to x.

To find: differentiation of with respect to x

⇒ y = a + b

Taking log both the sides:

{∵ log x^a = alog x}

Differentiating with respect to x:

Taking log both the sides:

{log x^a = alog x}

Differentiating with respect to x:

Hence, differentiation of (x.cos x)^x + with respect to x is (x cos x)^x{1 – x tan x + log(x cos x)} +