<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Let&nbsp;\(\mathrm{f}(x) = \ln x\). Show that&nbsp;\(\mathrm{f}'(x) = \frac{1}{x}\) by using differentiation from first principles.</span></div></li><li><div class="list-item-paragraph">Let&nbsp;\(\mathrm{g}(x) = \log_a x\), where&nbsp;\(a &gt; 0\) and \(a \neq 1\). Hence, or otherwise, show that&nbsp;\(\mathrm{g}'(x) = \frac{1}{x \ln a}\).</div></li></ol>

Let \(\mathrm{f}(x) = \ln x\). Show that \(\mathrm{f}'(x) = \frac{1}{x}\) by using differentiation from first principles.

Let \(\mathrm{g}(x) = \log_a x\), where \(a > 0\) and \(a \neq 1\). Hence, or otherwise, show that \(\mathrm{g}'(x) = \frac{1}{x \ln a}\).

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions