Differentiate each of the following with respect to $x$. $y = \sqrt{x + \frac{1}{x}}$ \(y = \fra

Question

Differentiate each of the following with respect to $x$. $y = \sqrt{x + \frac{1}{x}}$ $y = \frac{2}{\left(x^{2} + 1\right)^{3}}$ $y = \left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)^{2}$ $y = \left(\frac{x^{4}}{2} + \frac{2}{x^{4}}\right)^{4}$

Accepted Answer

(i) $\dfrac{1-x^{-2}}{2\sqrt{x+x^{-1}}}$ (ii) $-\dfrac{12x}{(x^2+1)^4}$ (iii) $1-\dfrac1{x^2}$ (iv) $4\left(\dfrac{x^4}{2}+\dfrac{2}{x^4}\right)^3\left(2x^3-\dfrac8{x^5}\right)$

Differentiation - Power Rule and Derivatives of Algebraic Functions

Differentiation - Power Rule and Derivatives of Algebraic Functions

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