Answer:
[tex]y' = (\frac{1}{4})^{x}*\ln{\frac{1}{4}} = -1.3863 *(\frac{1}{4})^{x}[/tex]
Step-by-step explanation:
If we a function in the following format:
[tex]y = a^{x}[/tex]
This function has the following derivative:
[tex]y' = a^{x}*\ln{a}[/tex]
In this problem, we have that:
[tex]y = (\frac{1}{4})^{x}[/tex]
So [tex]a = \frac{1}{4}[/tex]
The derivative is
[tex]y' = (\frac{1}{4})^{x}*\ln{\frac{1}{4}} = -1.3863 *(\frac{1}{4})^{x}[/tex]
