**1**Recognize the processes of change and variation in a function.**1.1**Identify the correlation between variables.**1.2**Break the curve into an infinite set of tangent lines.**1.3**Recognize the slope as a rate of change between variables.**1.4**Find the average rate of change for a function in a given interval.

**2**Calculate the derivative of a function.**2.1**Use definitions to calculate the derivative of a function.**2.2**Apply algebraic processes to develop derivatives.**2.3**Calculate the derivative of a function.

**3**Explore other ways to find derivatives.**3.1**Research about Caratheodory´s method to calculate derivatives.**3.2**Apply Caratheodory´s method to find derivatives for polynomic functions.**3.3**Suggest a reason for the viability of the method.**3.4**Find out why Caratheodory´s method works to get derivatives.**3.5**Tell the reason why Caratheodory´s method works.

**4**Identify the derivatives rules.**4.1**Recognize generalization processes for different deriving cases.**4.2**Recognize the derivatives rules.**4.3**Apply the derivatives rules.

**5**Apply the concept of derivatives to graph and solve problems.**5.1**Find the first and second derivatives of a function.**5.2**Sketch graphs using the concept of a derivative.**5.3**Apply the concept of derivatives to find the maximum and minimum values in a function.

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