Given that $y = \mathrm{e}^x (1 + \cos x)$, show \(\frac{\mathrm{d}y}{\mathrm{d}x} = \mathrm{

Question

Given that $y = \mathrm{e}^x (1 + \cos x)$, show $\frac{\mathrm{d}y}{\mathrm{d}x} = \mathrm{e}^x (1 + \cos x - \sin x)$.[1] Hence find $\int \mathrm{e}^x (\cos x - \sin x) \, \mathrm{d}x$.[3]

Accepted Answer

(b) $\displaystyle e^x\cos x+C$

2025 CGSS PRELIMS P1 Q12

2025 CGSS PRELIMS P1 Q12

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