Techniques of Differentiation - Quotient Rule

Techniques of Differentiation - Quotient Rule

Differentiate the following with respect to \(x\):

\(\sqrt{4x^{2}-3x}\)
\(\sqrt{x^{2}-4x}\)
\(\sqrt{\frac{x}{x^{2}-1}}\)

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Answer:(i) \(\frac{8x-3}{2\sqrt{4x^2-3x}}\) (ii) \(\frac{x-2}{\sqrt{x^2-4x}}\) (iii) \(-\frac{x^2+1}{2(x^2-1)^2\sqrt{x/(x^2-1)}}\)

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