- Any materials in this notes is not required in the scope of the course, but is included for your understanding.

#### Estimating Derivatives

- After an extensive study of limit notations, continuity and differentiability, it is clear the derivatives is simply a limit notation, and there can be estimated as the value as x approaches a certain value.
- This is useful when the function given is too difficult to obtain its derivative from first principles, or by directly differentiating (however, after “
**Derivatives of Functions**” and “**Differentiation Rules**” sections in A3 – Calculus this problem should not exist anymore).

Example

If f(x)=3^{x}, find f^{\prime}(2.4), accurate to 3 decimal places

As a sneak peak, the answer is 3^{2.4} \ln 3=15.344(3 \mathrm{~d} \cdot \mathrm{p} \cdot)

We can estimate f^{\prime}(2.4) numerically by the following: