Question

derivative of ln(2x)/2x

Answer 1

d/dx ln x = 1/x * d/dx x. Use the product rule and chain rule.

d/dx ln(2x) = 1/2x * d/dx 2x = 1/2x * 2.

Using the product rule:

d/dx ln(2x) / 2x = d/dx ln(2x) * 2x + ln(2x) * d/dx 2x = 1/2x * 2 + ln(2x) * 1/(2x)^2

Answer 2

thats whole thing is the answer?

Answer 3

It depends if you understand the answer. You should probably show how you know what the derivative is. ln(2x)/2x is the product of two functions of x: ln(2x) and 2x. If you're asking how to find the derivative of that, then I assume you're just studying derivative rules. Therefore, for this problem you should apply the chain rule and the derivative rule, while also knowing the way to calculate the derivate for the ln x function and a polynomial like 2x. If you combine all of those, like I did above then you'll reach the answer.