Find the derivatives of the following functions with respect to $x$: \(y = \log_{2}\left( \frac{x}

Question

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

Accepted Answer

(i) $\frac1{\ln2}\left(\frac1x-\frac1{x-1}\right)$ (ii) $\frac1{\ln5}\left(\frac2x+3\tan x\right)$ (iii) $\frac1{\ln3}\left[-\frac1{2(1-x)}-\frac{\sec^2x}{\tan x}\right]$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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