Diffrentiation of natural logs (ln)

1. Sep 14, 2010

chanella35

the question is: differentiate wiith repsect to x:

(ln(5x))^1/5

i differentiated and got :

1/5ln(5x)

y'=1/5x

I dont think this is correct. The answer should be ln5/5.

Can anyone help me?

chanella

2. Sep 14, 2010

logarithmic

That's not right. The answer shouldn't be ln5/5, because that's a number. The answer should be a function.

Use the chain rule: power to the front, subtract 1, multiply by the derivative of what's inside the bracket.

3. Sep 14, 2010

chanella35

y'=1/5 (5)(ln5x)^(1/5-1)

y'= (ln5x)^-4/5

is this right??

Thanks for helping :)

4. Sep 14, 2010

logarithmic

Almost. The derivative of ln(f(x)) is f'(x)/f(x), so the derivative of ln(5x) is 5/(5x) = 1/x.

So replacing (5) with (1/x), then simplifying is the correct answer.