Question

What is the derivative of `((8^x)^5)^x`?

Answer 1

`10x((8^x)^5)^x ln8`

Explanation:

`((8^x)^5)^x = 8^(5x^2)`.

So,

`d/dx(((8^x)^5)^x ) = d/dx(8^(5x^2))`.

Now use `d/dx(8^u) = 8^u lnu d/dx(u)` to get

`d/dx(8^(5x^2)) = 8^(5x^2) ln8 d/dx(5x^2)`

`= 8^(5x^2) ln8 (10x)`

`= 10x 8^(5x^2) ln8`