Evaluate each of the following. $\frac{\mathrm{d}}{\mathrm{d}x}(\ln \cos 3x)$ \(\frac{\mathrm{d}}{

Question

Evaluate each of the following. $\frac{\mathrm{d}}{\mathrm{d}x}(\ln \cos 3x)$ $\frac{\mathrm{d}}{\mathrm{d}x}(\ln \sin 4x)$ $\frac{\mathrm{d}}{\mathrm{d}x}\left[\ln \left(2x^4 - \cos 3x^5\right)\right]$ $\frac{\mathrm{d}}{\mathrm{d}x}[\ln (\tan x - \sin x)]$

Accepted Answer

(i) $-3\tan 3x$ (ii) $4\cot 4x$ (iii) $\dfrac{8x^3+15x^4\sin 3x^5}{2x^4-\cos 3x^5}$ (iv) $\dfrac{\sec^2x-\cos x}{\tan x-\sin x}$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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