<p>It is given that&nbsp;\(y = x^{xy}\), where&nbsp;\(x &gt; 0\), \(y &gt; 0\).</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Show that&nbsp;\(\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{y^2 (1 + \ln x)}{1 - \ln y}\).<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Hence find the coordinates of the point on the curve \(y = x^{xy}\) whose tangent is parallel to the \(y\)-axis.<span class="inline-marks">[2]</span></div></li></ol>

It is given that \(y = x^{xy}\), where \(x > 0\), \(y > 0\).

Show that \(\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{y^2 (1 + \ln x)}{1 - \ln y}\).

Hence find the coordinates of the point on the curve \(y = x^{xy}\) whose tangent is parallel to the \(y\)-axis.

Applications of Differentiation

International Baccalaureate Higher Level Mathematics

22025 ACJC P1 Q3

22025 ACJC P1 Q3