What is the 'chain rule'?

The chain rule is incredibly useful when differentiating compositions of funcions. 

 

Until now you have really only met dy/dx as your derivative. By imagining dy/dx as a fraction, you can transform it into something using another parameter, for example t.

 

For example, just how 1/2 x 2/3 = 2/6 (multiply numerater, multiply denominator), dy/dx x dt/dy = dydt/dxdy, and the 'dy' values would cancel, giving dt/dx. This is only for this level of mathematics however, as in reality, you can't treat dy/dx as a fraction!