Question

if y=log_ x then dy/dx=

Answer 1

$</p><p> \sf \rightarrow \quad y = log \: x \\ \\ \sf \rightarrow \quad y = \frac{ log_{e} \: x }{ log_{e} \: 10 } \\ \\ \sf \rightarrow \quad y = \frac{ ln \: x }{ ln \: 10 } \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{d}{dx} \left( \frac{ ln \: x }{ ln \: 10 } \right) \\ \\ </p><p>\sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{ ln \: 10 } \frac{d(ln \: x)}{dx} \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{ ln \: 10} \: \cdot \: \frac{1}{x} \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{x \cdot ln \: 10} </p><p>$