Chain Rule

Short description and context

Chain Rule

The derivative of a function of a function, i.e. $f(x) = g[h(x)]$, with respect to $x$ is given by the chain rule: $$ \frac{\textrm{d}f(x)}{\textrm{d}x} = \frac{\textrm{d}g[h(x)]}{\textrm h(x)} \frac{\textrm{d}h(x)}{\textrm{x}} $$

Syllabus Aims

  • You should be able to write out the chain rule.
  • You should be able to use the chain rule to find the derivatives of functions of functions.
  • You should be able to use the chain rule in tandem with the product rule to find the derivatives of complicated function.

Worked examples

Description and link

Module

Author

Problems that require you to use the chain rule and the product rule in tandem PHY9038 G. Tribello

Contact Details

School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN

Email: g.tribello@qub.ac.uk
Website: mywebsite