Calculus/Differentiation/Differentiation Defined/Solutions

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1. Find the slope of the tangent to the curve at .

The definition of the slope of at is
Substituting in and gives:

2. Using the definition of the derivative find the derivative of the function .

3. Using the definition of the derivative find the derivative of the function . Now try . Can you see a pattern? In the next section we will find the derivative of for all .

4. The text states that the derivative of is not defined at . Use the definition of the derivative to show this.


Since the limits from the left and the right at are not equal, the limit does not exist, so is not differentiable at .

6. Use the definition of the derivative to show that the derivative of is . Hint: Use a suitable sum to product formula and the fact that and .

  • Find the derivatives of the following equations:
7.

8.

9.