`y = 5^(-4x)` Find the derivative of the function

`y=5^(-4x)`

The derivative formula of an exponential function is:

`d/(dx) (a^u) = ln(a) * a^u * (du)/(dx)`

Applying this formula, the derivative of the function is:

`(dy)/(dx) = d/(dx)(5^(-4x))`

`(dy)/(dx) = ln(5) * 5^(-4x) * d/(dx)(-4x)`

`(dy)/(dx) = ln(5) * 5^(-4x) * (-4)`

`(dy)/(dx) = -4 ln(5) * 5^(-4x)`

Therefore, `(dy)/(dx) = -4ln(5) * 5^(-4x)` .