How do you differentiate the following parametric equation:  x(t)=lnt, y(t)=(t-3) ?

May 23, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = t$

Explanation:

The derivative $\frac{\mathrm{dy}}{\mathrm{dx}}$of parametric equations is.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{dt}}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

here x = lnt $\Rightarrow \frac{\mathrm{dx}}{\mathrm{dt}} = \frac{1}{t}$

and $y = t - 3 \Rightarrow \frac{\mathrm{dy}}{\mathrm{dt}} = 1$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{\frac{1}{t}} = 1 \times \frac{t}{1} = t$