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Determine $\frac{dy}{dx}$ for each of the following cases

  1. $y = x^{3} - \frac{3}{x}$
  2. $y = (x - 1)(3x + 1)$
  3. $y = \frac{2\sqrt{x} -5}{\sqrt{x}}$
in Mathematics by Diamond (60,604 points) | 42 views

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1.$ = x^3 - 3x^-1 , \dfrac{dy}{dx }= 3x^2 + 3x^-2 = 3x^2 + \dfrac{3}{x^2}$

2. Expand and simplify $= 3x^2 -2x -1, \dfrac{dy}{dx} = 6x -2$

3. $(\dfrac{2x^1}{2} -5).x^{-\dfrac{1}{2}}$

  $= 2 - 5x^{- \dfrac{1}{2}}$

$\dfrac{dy}{dx} = \dfrac{ \dfrac{5x^-3}{2}}{2} = \dfrac{5}{2\sqrt{(x)^3}}$
by Diamond (42,256 points)
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