Changes

The chain rule can also be applied to multivariable functions. The derivative of a multivariable function is expressed as follows:

The chain rule can also be applied to multivariable functions. The derivative of a multivariable function is expressed as follows:

<math> \frac {d}{dt}(f(x(t), y(t))) = \frac{\partial f}{dx}\times \frac{dx}{dt} + \frac{\partial f}{dy}\times \frac{dy}{dt} </math>

<math> \frac {d}{dt}(f(x(t), y(t))) = \frac{\partial f}{\partial x}\times \frac{dx}{dt} + \frac{\partial f}{\partial y}\times \frac{dy}{dt} </math>

or in vector notation:

or in vector notation: