Find , when

1y = e^x + 10^x + x^x

let y = e^x + 10^x + x^x

⇒ y = a + b + c

where a= e^x; b = 10^x ; c = x^x

a= e^x

Taking log both the sides:

⇒ log a= log e^x

⇒ log a= x log e

{log x^a = alog x}

⇒ log a= x {log e =1}

Differentiating with respect to x:

Put the value of a = e^x

b = 10^x

Taking log both the sides:

⇒ log b= log 10^x

⇒ log b= x log 10

{log x^a = alog x}

Differentiating with respect to x:

Put the value of b = 10^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