Question

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

y = (1/4)^x

Answer 1

`y' = ((1)/(4))^(x)*\ln{(1)/(4)} = -1.3863 *((1)/(4))^(x)`

Explanation:

If we a function in the following format:

`y = a^(x)`

This function has the following derivative:

`y' = a^(x)*ln(a)`

In this problem, we have that:

`y = ((1)/(4))^(x)`

So
`a = (1)/(4)`

The derivative is

`y' = ((1)/(4))^(x)*\ln{(1)/(4)} = -1.3863 *((1)/(4))^(x)`