Question

Differentiate the following function with respect to x :

10^(10x)

Answer 1

Let y = 10^10x

Taking log both the sides:

⇒ log y = log 10^10x

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

⇒ log y = (10log 10)x

Differentiating with respect to x:

{Here 10log (10) is a constant term}

{Using chain rule, \(\cfrac{d(au)}{d\text x}=a\cfrac{du}{d\text x}\) where a is any constant and u is any variable}