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

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

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

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.

Techniques of Differentiation

International Baccalaureate Higher Level Mathematics

2025 ACJC P1 Q3

2025 ACJC P1 Q3