Question

How do you find the derivative of `y = (ln 2)^x`?

Answer 1

`(ln (ln 2))(ln 2)^x`

Explanation:

Use `a^x=e^(x ln a) and d/dx(e^(ax))=a e^(ax)`.

Here, a=ln 2.

`y'= (e^((ln (ln 2)) x))'=ln( ln 2) e^(ln 2 x)=ln (ln 2) (ln 2)^x`
ln 2 = 0.6931 and ln (ln 2)=-0.3665, nearly..

Interestingly, the nth derivative is `(ln (ln 2))^n(ln 2)^x`
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