Answer:
Therefore, the derivative dy/dx of y = ln(4x) is 1/x.
To find dy/dx if y = ln(4x), we can use the chain rule of differentiation.
Let’s start by differentiating y with respect to x. Recall that the derivative of ln(u) with respect to u is 1/u.
dy/dx = d/dx ln(4x)
Using the chain rule, we need to multiply the derivative of the logarithmic function ln(u) with respect to u by the derivative of the inner function (4x) with respect to x.
dy/dx = (1/(4x)) * d/dx (4x)
The derivative of 4x with respect to x is simply 4, as the derivative of any constant multiplied by x is that constant.
dy/dx = (1/(4x)) * 4
Simplifying further:
dy/dx = 1/x
Therefore, the derivative dy/dx of y = ln(4x) is 1/x.