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let y = xⁿ + n^x + x^x + nⁿ

⇒ y = a + b + c + m

where a= xⁿ; b = n^x ; c = x^x ; m= nⁿ

a= xⁿ

Taking log both the sides:

⇒ log a= log xⁿ

⇒ log a= n log x

{log x^a = alog x}

⇒ log a= n log x {log e =1}

Differentiating with respect to x:

Put the value of a = xⁿ

b = n^x

Taking log both the sides:

⇒ log b= log n^x

⇒ log b= x log n

{log x^a = alog x}

Differentiating with respect to x:

Put the value of b = n^x:

c = x^x

Taking log both the sides:

⇒ log c= log x^x

⇒ log c= x log x

{log x^a = alog x}

Differentiating with respect to x:

Put the value of c = x^x

m = nⁿ