Techniques of Differentiation - Derivatives of Trigonometric Functions
Techniques of Differentiation - Derivatives of Trigonometric Functions
TGM Original Questions
Find the derivative of each of the following with respect to \(x\).
- \(y = 6 \sin(4x^3 - x) - 4 \tan 3x^2\)
- \(y = \tan 5x^3 - \cos(x^2 + x) - 8\)
- \(y = 3x^2 - \tan\left(\frac{\pi}{3} - \frac{x}{3}\right)\)
- \(y = 7x^3 - 2 \cos\left(\frac{\pi}{5}x - 3\right)\)
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Answer:(i) \(6(12x^2-1)\cos(4x^3-x)-24x\sec^2(3x^2)\) (ii) \(15x^2\sec^2(5x^3)+(2x+1)\sin(x^2+x)\) (iii) \(6x+\dfrac13\sec^2\left(\dfrac{\pi}{3}-\dfrac{x}{3}\right)\) (iv) \(21x^2+\dfrac{2\pi}{5}\sin\left(\dfrac{\pi x}{5}-3\right)\)
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