Find the derivative of each of the following w.r.t $x$: $y = \ln (\sin x \cos^3 x)$ \(y = \ln (\

Question

Find the derivative of each of the following w.r.t $x$: $y = \ln (\sin x \cos^3 x)$ $y = \ln (\tan 3x^4 + \sin 4x)$ $\mathrm{f}(x) = \ln \left( \sqrt{\frac{2-\sin x}{\tan^3 x}} \right)$

Accepted Answer

(a) $\cot x-3\tan x$ (b) $\frac{12x^3\sec^2(3x^4)+4\cos(4x)}{\tan(3x^4)+\sin(4x)}$ (c) $\frac12[-\frac{\cos x}{2-\sin x}-\frac{3\sec^2x}{\tan x}]$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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