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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=4\text{t, y}=\frac{4}{\text{t}}$
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Answer

The given equations are $\text{x}=4\text{t, and y}=\frac{4}{\text{t}}$
$\frac{\text{dx}}{\text{dt}}=\frac{\text{d}}{\text{dt}}(4\text{t)}=4$
$\frac{\text{dy}}{\text{dt}}=\frac{\text{d}}{\text{dt}}\Big(\frac{4}{\text{t}}\Big)=4.\frac{\text{d}}{\text{dt}}\Big(\frac{1}{\text{t}}\Big)=4.\Big(\frac{-1}{\text{t}^2}\Big)=\frac{-4}{\text{t}^2}$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\Big(\frac{\text{dy}}{\text{dt}}\Big)}{\Big(\frac{\text{dx}}{\text{dt}}\Big)}=\frac{\Big(\frac{-4}{\text{t}^2}\Big)}{4}=\frac{-1}{\text{t}^2}$

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