Question

If n > 1 and y = log n x, find dy/dx.

Answer 1

Did you mean \(y=\log(nx)\)?

Answer 2

If so, recall that the derivative of \(\ln(x)\) is \(\frac{1}{x}\) and use the chain rule.

Answer 3

(Assuming you're using \(\log\) to mean the natural logarithm, not base 10.)

Answer 4

ah, n is actually the base! \[\log_{n}x\]

Answer 5

Oh, then the rule to use is \(\log_a(b)^{\prime} = \frac{1}{x\ln(a)}\).

Answer 6

I started with a b and ended with an x there, sorry.

Answer 7

So in your case you would get
\[\frac{1}{x\ln(n)}\]

Answer 8

okay, i understand now! thank you. the n instead of a constant confused me.

Answer 9

You can treat any variables besides the one you're taking a derivative with respect to as constants.

Answer 10

(As long as they aren't functions of your variable, \(y(x)\) obviously isn't a constant.)