Find the derivative of each of the following functions with respect to $x$. \(f(x) = \ln \left(\co

Question

Find the derivative of each of the following functions with respect to $x$. $f(x) = \ln \left(\cos^2 3x \tan^3 3x\right)$ $f(x) = \ln \left(\tan^2 x \sqrt{\cos x}\right)$ $f(x) = \ln \sqrt{\frac{2 - \sin x}{\tan^3 x}}$ $f(x) = \ln \sqrt{\frac{\cos 2x}{\tan^2 x}}$

Accepted Answer

(i) $-6\tan 3x+9\dfrac{\sec^2 3x}{\tan 3x}$ (ii) $2\dfrac{\sec^2x}{\tan x}-\dfrac12\tan x$ (iii) $-\dfrac{\cos x}{2(2-\sin x)}-\dfrac32\dfrac{\sec^2x}{\tan x}$ (iv) $-\tan 2x-\dfrac{\sec^2x}{\tan x}$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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