Parametric Differentiation
To differentiate parametric equations, we must use the chain rule.
Example
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:
Image
Example
To find the second derivative in the above example, therefore:
d2y = d(1/t) × dt
dx2 dt dx
= -1 × 1 .
t2 4at
