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Q)

Find the differential of the functions. $y$=$\large\frac{x-2}{2x+3}$

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A)
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  • Let $y=f(x)$ be a differentiable function then the quantities $dx$ and $dy$ are called differentials.The differential $dx$ is an independent variable.
  • The differential $dy$ is then defined by $dy=f'(x)dx(dx \approx \Delta x)$
  • Also $f(x+\Delta x)-f(x)=\Delta y =dy $ from which $f(x+\Delta x) $can be evaluated
Given $y=\large\frac{x-2}{2x+3}$
$dy=\large\frac{(2x+3)(1)-(x-2)(2)}{(2x+3)^2}$$dx$
$\quad=\large\frac{7}{(2x+3)^2}$$dx$
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