Introduction

In this Section we will see how to obtain the derivative of a composite function (often referred to as a ‘function of a function’). To do this we use the chain rule . This rule can be used to obtain the derivatives of functions such as $e^{x^2+3x}$ (the exponential function of a polynomial); $sin\left(lnx\right)$ (the sine function of the natural logarithm function); $\sqrt{x^3+4}$ (the square root function of a polynomial).

Prerequisites

• be able to differentiate standard functions
• be able to use the product and quotient rule for finding derivatives

Learning Outcomes

• differentiate a function of a function
  
  using the chain rule
• differentiate a power function