`y = log_4(5x+1)` Find the derivative of the function

`y=log_4(5x + 1)`

The derivative formula of a logarithm is:

`d/(dx) [log_a (u)] = 1/(ln(a) * u) * (du)/(dx)`

Applying that formula, the derivative of the function will be:

`(dy)/(dx) = d/(dx)[ log_4(5x+1)]`

`(dy)/(dx) =1/(ln(4) * (5x+1))* d/(dx) (5x+1)`

`(dy)/(dx) =1/(ln(4) * (5x+1)) * 5`

`(dy)/(dx) =5/((5x+1)ln(4))`

Therefore, the derivative of the function is `(dy)/(dx) =5/((5x+1)ln(4))` .