Question

Differentiate the function with respect to x: 10^{(10^x)}

Answer 1

Suppose y = 10^{(10^x)}

On taking log both sides

log y = log 10^{(10^x)}

log y = 10 x log 10 {log x^a = a log x}

log y = (10 log 10)x

On differentiating with respect to x

Now, here 10 log 10 is a constant term, so on using chain rule,

As we know that