How do you use the chain rule?

The chain rule is used to differentiate when there is a function within another function. For example y=(4x+6)^0.5, y=(x+1)³The general formula for the chain rule is dy/dx= dy/du * du/dxAn example of this is differentiate y=(2x+3)³Let u= 2x +3 this means y = u³differentiate each term ...du/dx = 2. dy/du = 3u². so dy/dx = dy/ du * du/dx = 3u² * 2 = 6u²substitute the expression for u back into the equation so that it is in terms of x. dy/dx = 6(2x+3)²