Question

differentiate $f(t)=(ln 2)^t$.
$f(t)=$

Explanation:

Step1: Recall exponential - function derivative formula

The derivative of $a^t$ with respect to $t$ is $a^t\ln a$, where $a>0,a
eq1$. Here $a = \ln 2$.

Step2: Apply the formula

For $f(t)=(\ln 2)^t$, by the formula $\frac{d}{dt}(a^t)=a^t\ln a$, we have $f'(t)=(\ln 2)^t\ln(\ln 2)$.

Answer:

$(\ln 2)^t\ln(\ln 2)$