Connected Rates of Change (Cambridge International IGCSE Further Maths)

Connected rates of change

What are connected rates of change?

• In situations involving more than two variables you can use the chain rule to connect multiple rates of change into a single equation

• Look out for the word "rate"

  • This implies a derivative is involved
  • e.g. The height is increasing at a rate of 4 cm per second means $\frac{dh}{dt}=4$

• If the variable is decreasing then the rate will be negative

  • e.g. The height is decreasing at a rate of 4 cm per second means $\frac{dh}{dt}=-4$

Exam Hint

• These problems can involve a lot of letters

  • be sure to keep track of what they all refer to

• Be especially sure that you are clear about which letters are variables and which are constants

  • these behave very differently when differentiation is involved!

Worked Example