Find the derivatives of the following functions with respect to $x$: \(y = \ln \left( \frac{\tan^{

Question

Find the derivatives of the following functions with respect to $x$: $y = \ln \left( \frac{\tan^{3}(1 - e^{x})}{\ln x^{3}} \right)$ $y = \ln \left( \frac{x^{5}}{\sin^{2}x} \right)$ $y = \ln \left( \frac{\ln x^{3}}{\tan x} \right)$

Accepted Answer

(i) $-\frac{3e^x\sec^2(1-e^x)}{\tan(1-e^x)}-\frac1{x\ln x}$ (ii) $\frac5x-2\cot x$ (iii) $\frac1{x\ln x}-\frac{\sec^2x}{\tan x}$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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