Parametric Derivatives

In a function, we may have the dependent variables x and y which are dependent on the third independent variable. If x = f(t) and y = g(t), then derivative is calculated as dy/dx = f'(x)/g'(x). Suppose, if x = 4 + t² and y = 4t² -5t⁴ , then let us find the parametric derivative.

dx/ dt = 2t and dy/dt = 8t -20t³

dy/dx = (dy/dt)/(dx/dt)

dy/dx = (8t -20t³ )/2t

=2t(4-10t² )/2t

dy/dx = 4-10t²