What are the first and second derivatives of $f(x)=ln (6^x)$ ?

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Answer 1 · 2015-12-28T21:06:17

We'll resort to chain rule here.

Chain rule states that $(dy)/(dx)=(dy)/(du)(du)/(dx)$

Renaming $u=6^x$ , we can start:

$(dy)/(du)=1/u$

$(du)/(dx)=6^xln(6)*1=6^xln(6)$

$(dy)/(dx)=(6^x*ln(6))/6^x=ln(6)$

As $ln(6)$ is a constant, its derivative is zero.

What are the first and second derivatives of f(x)=ln (6^x)f(x)=ln (6^x)?