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  • Find dy/dx of each of the functions expressed in parametric form in x=t+1/t

Find \frac{dy}{dx} of each of the functions expressed in parametric form in
x=t+\frac{1}{t}\: \: ,\: \: y=t-\frac{1}{t}

Answers (1)

We have given, two parametric equation,

x=t+\frac{1}{t}\: \: ,\: \: y=t-\frac{1}{t}

Now, differentiate both equation w.r.t x

We know, \frac{d}{d x}\left(\frac{1}{x}\right)=-\frac{1}{x^{2}}$ and $\frac{d}{d x}(x)=1
So,
\frac{d x}{d t}=1-\frac{1}{t^{2}}
and,
\frac{d y}{d x}=1+\frac{1}{t^{2}}
Now,

\begin{aligned} &\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}\\ &\frac{d y}{d x}=\frac{1+\frac{1}{t^{2}}}{1-\frac{1}{t^{2}}}\\ &\text { Hence, }\\ &\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{t}^{2}+1}{\mathrm{t}^{2}-1} \end{aligned}

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infoexpert22

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