Differentiate each of the following with respect to $x$. $y = e^x \sin 2x$ \(y = \frac{e^x \cos

Question

Differentiate each of the following with respect to $x$. $y = e^x \sin 2x$ $y = \frac{e^x \cos x}{e^{\frac{x}{2}}}$ $y = e^{3x-1}(\cos x - \sin x)$ $y = 3e^{\sqrt{x}} \sin 2x$

Accepted Answer

(i) $\mathrm e^x(\sin 2x+2\cos 2x)$ (ii) $\mathrm e^{x/2}\left(\dfrac12\cos x-\sin x\right)$ (iii) $2\mathrm e^{3x-1}(\cos x-2\sin x)$ (iv) $3\mathrm e^{\sqrt{x}}\left(\dfrac{\sin 2x}{2\sqrt{x}}+2\cos 2x\right)$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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