Find the derivative of each of the following w.r.t $x$: \(y = \ln \left( \frac{\sqrt{x}}{x^2 - 1}

Question

Find the derivative of each of the following w.r.t $x$: $y = \ln \left( \frac{\sqrt{x}}{x^2 - 1} \right)$ $y = \ln \left( \frac{x^2 + 1}{x - 1} \right)$ $y = \ln \left( \frac{\cos x}{1 - \sin x} \right)$

Accepted Answer

(a) $\dfrac1{2x}-\dfrac{2x}{x^2-1}$ (b) $\dfrac{2x}{x^2+1}-\dfrac1{x-1}$ (c) $\sec x$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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