How do you differentiate $y = ln (\frac{10}{x})$ $y=ln(10/x)$ ?

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How do you differentiate $y = ln (\frac{10}{x})$ $y=ln(10/x)$ ?

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Answer 1 · 2016-09-10T23:23:24

$\frac{d y}{d x} = - \frac{1}{x}$ $dy/dx=-1/x$

Explanation:

We need to know that:

$log (\frac{A}{B}) = log (A) - log (B)$ $log(A/B)=log(A)-log(B)$
$\frac{d}{d x} ln (x) = \frac{1}{x}$ $d/dxln(x)=1/x$
$\frac{d}{d x} (constant) = 0$ $d/dx("constant")=0$

Thus:

$y = ln (\frac{10}{x})$ $y=ln(10/x)$

$y = ln (10) - ln (x)$ $y=ln(10)-ln(x)$

$\frac{d y}{d x} = 0 - \frac{1}{x}$ $dy/dx=0-1/x$

$\frac{d y}{d x} = - \frac{1}{x}$ $dy/dx=-1/x$

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How do you differentiate $y = ln (\frac{10}{x})$ $y=ln(10/x)$ ?

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