The bchain rule/b is used for differentiating composite functions and topic=7/80connected rates of change/topic.

(y = f\big(g(x)\big) )

(\boxed{\dfrac{dy}{dx} = f'\big(g(x)\big)g'(x)} )

Using substitution, if (y = f(u) ) and (u = g(x) ), then:

(\boxed{\dfrac{dy}{dx} = \dfrac{dy}{du} × \dfrac{du}{dx}} )

Tip: Think of it as: "ithe derivative of the 'outside' function, multiplied by the derivative of the 'inside' function/i".

The chain rule can be "chained" for more than two functions. For three functions, if (y = f(u) ), (u = g(v) ) and (v = h(x)), then:

(\dfrac{dy}{dx} = \dfrac{dy}{du} × \dfrac{du}{dv} × \dfrac{dv}{dx} )