Given that $y={{x}^{\cos x}}$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ only. [3] A cu

Question

Given that $y={{x}^{\cos x}}$, find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ only. [3] A curve has equation ${{x}^{2}}y-x{{y}^{2}}=6$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$. [2] Find the exact coordinates of the point on the curve where $\frac{\mathrm{d}y}{\mathrm{d}x}=1$. [5]

Accepted Answer

(a) $\dfrac{\mathrm dy}{\mathrm dx}=x^{\cos x-1}(\cos x-x\sin x\ln x)$ (b)(i) $\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2-2xy}{x^2-2xy}$ (b)(ii) $\left(-\sqrt[3]{3},\sqrt[3]{3}\right)$

2024 YIJC Promo Q4

2024 YIJC Promo Q4

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