Parametric equations are a set of equations which both depend on the same variable, such as t. An example of this would be:

x = 2t²+1 and y = t⁴-2

As the value of t changes the equations will give you seperate values for x and for y which can be plotted on a coordinate grid.

To differentiate a parametric equation you must first differentiate both the equation for x and for y seperately with respect to t. So in this case it would be:

dx/dt = 4t and dy/dt = 4t³

We now have dx/dt and dy/dt. By simply divding dy/dt by dx/dt we get dy/dx as the dt cancels in the division (Since dividing is the same as multiplying by the reciprocal so (dy/dt)/(dx/dt) = (dy/dt)x(dt/dx) = dy/dx).

So for our example:

(dy/dt)/(dx/dt) = 4t³/4t = t² = dy/dx.

find dy/dx= x^2 +x^3

Related Maths A Level answers

Given that y = 4x^3 – 5/(x^2) , x =/= 0, find in its simplest form dy/dx.

How do you differentiate parametric equations?

Differentiate the following... f(x)= 5x^4 +16x^2+ 4x + 5

Find the derivative of yx+5y-sin(y) = x