Evaluate each of the following. \(\frac{\mathrm{d}}{\mathrm{d}x}\left[ \ln \left( \sin x \cos^3 x \r

Question

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

Accepted Answer

(i) $\cot x-3\tan x$ (ii) $\dfrac{12x^3\sec^2(3x^4)+4\cos 4x}{\tan 3x^4+\sin 4x}$ (iii) $-\tan x+\dfrac32\dfrac{\sec^2x}{\tan x}$ (iv) $-2\tan x+\dfrac12\cot x$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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