Question

Y = log₂x

find dy/dx

Answer 1

$\sf \rightarrow \quad y = log_{2}x \\ \\ \sf \rightarrow \quad y = \frac{ln \: x}{ln \: 2} \qquad \bigg( \: \because \: \: log_{m}n = \frac{ log_{a}(n) }{ log_{a}(m) } \: \bigg) \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{ln \: 2} \cdot \frac{d(ln \: x)}{dx} \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{ln \: 2} \cdot \frac{1}{x} \\ \\ \sf \rightarrow \quad \frac{dy}{dx} = \frac{1}{x \cdot ln \: 2}$