# How do you find the derivative of #ln(10/x)#?

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To find the derivative of ( \ln\left(\frac{10}{x}\right) ) with respect to (x), you apply the chain rule:

[ \frac{d}{dx}[\ln(u)] = \frac{1}{u} \cdot \frac{du}{dx} ]

In this case, (u = \frac{10}{x}).

[ \frac{du}{dx} = \frac{d}{dx}\left(\frac{10}{x}\right) = -\frac{10}{x^2} ]

Therefore, the derivative of ( \ln\left(\frac{10}{x}\right) ) with respect to (x) is:

[ \frac{d}{dx}\left[\ln\left(\frac{10}{x}\right)\right] = \frac{1}{\frac{10}{x}} \cdot \left(-\frac{10}{x^2}\right) = -\frac{x}{10} \cdot \frac{-10}{x^2} = \frac{1}{x} ]

So, the derivative is ( \frac{1}{x} ).

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