Find the derivative of each of the following functions with respect to $x$. \(f(x) = \frac{e^{2-3x

Question

Find the derivative of each of the following functions with respect to $x$. $f(x) = \frac{e^{2-3x}}{\ln x}$ $f(x) = \ln \frac{\sqrt{x}}{x^2 - 1}$ $f(x) = \ln \frac{x^2 + 1}{x - 1}$ $f(x) = \ln \frac{\cos x}{1 - \sin x}$

Accepted Answer

(i) $-\dfrac{\mathrm e^{2-3x}\left(3\ln x+\frac1x\right)}{(\ln x)^2}$ (ii) $\dfrac{1}{2x}-\dfrac{2x}{x^2-1}$ (iii) $\dfrac{2x}{x^2+1}-\dfrac{1}{x-1}$ (iv) $\sec x$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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