Differentiate each of the following with respect to $x$. $y = 3\mathrm{e}^{\cos x} \cos x$ \(y =

Question

Differentiate each of the following with respect to $x$. $y = 3\mathrm{e}^{\cos x} \cos x$ $y = \mathrm{e}^{\sin x - \cos 2x}$ $y = 3x^5 \mathrm{e}^{\cos 5x}$ $y = 2x^2 \mathrm{e}^{1 - \tan x^2}$

Accepted Answer

(i) $-3\mathrm e^{\cos x}\sin x(\cos x+1)$ (ii) $(\cos x+2\sin 2x)\mathrm e^{\sin x-\cos 2x}$ (iii) $15x^4\mathrm e^{\cos 5x}(1-x\sin 5x)$ (iv) $-4x\mathrm e^{1-\tan(x^2)}(1-x^2\sec^2(x^2))$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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