Question

(1 point) Find dy/dx if y=ln(4x) Answer: You have attempted this problem 0 times. You have unlimited attempts remaining.

Answer 1

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.