It is given that $y={{x}^{xy}}$ , where $x0$, $y0$ . Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in ter

Question

It is given that $y={{x}^{xy}}$ , where $x>0$, $y>0$ . Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$. Hence find the equation of the tangent to the curve $y={{x}^{xy}}$which is parallel to the $y$-axis. [6]

Accepted Answer

$\frac{dy}{dx}=\frac{y^2(1+\ln x)}{1-xy\ln x}$; vertical tangent $x=1.32$

2012 HCI P1 Q3

2012 HCI P1 Q3

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