Parametric Differentiation

To differentiate parametric equations, we must use the chain rule.


If x = 2at2 and y = 4at, find dy/dx

dy = dy × dt
dx   dt   dx

In this case, dx/dt = 4at and so dt/dx = 1/(4at)

Also dy/dt = 4a. Hence:

dy/dx = 4a × 1/4at = 1/t

Finding the Second Derivative

Finding the second derivative is a little trickier.

We use the fact that:



To find the second derivative in the above example, therefore:

d2y = d(1/t) × dt

dx2    dt         dx

= -1 ×  1 .

   t2   4at

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