Find the derivative of each of the following with respect to $x$. $y = 4 \cos x \sin 3x$ \(y = \

Question

Find the derivative of each of the following with respect to $x$. $y = 4 \cos x \sin 3x$ $y = \sin^3(2x^2 - \mathrm{e})$ $y = \mathrm{cosec}^3(\pi x^4 + 1) - 3x^5$ $y = \sin \left( \mathrm{e}x + \frac{\pi}{4} \right) + \cos(2x^3 - 5x)$

Accepted Answer

(i) $12\cos x\cos 3x-4\sin x\sin 3x$ (ii) $12x\sin^2(2x^2-\mathrm e)\cos(2x^2-\mathrm e)$ (iii) $-12\pi x^3\operatorname{cosec}^4(\pi x^4+1)\cos(\pi x^4+1)-15x^4$ (iv) $\mathrm e\cos\left(\mathrm ex+\dfrac{\pi}{4}\right)-(6x^2-5)\sin(2x^3-5x)$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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