1. 4.1: Techniques for Differentiation Objectives: Students will be able to… Apply the constant and power rule for differentiation Apply the sum and difference rule for differentiation

2. The definition and interpretation of the derivative will NOT change, but we do have rules that make finding the derivative easier. Pay attention to variables used. If, the derivative would be g ‘(t) or Another notation for the derivative:

3. What is the slope of the function f(x) = 10? f(x) = -5?? f(x)= 15,000??  Constant slope, constant rate of change  Slope always 0 CONTSTANT RULE: THE DERIVATIVE OF A CONSTANT FUNCTION IS 0 If f(x)= k, where k is any real number, then f’(x)=0.

4. Find the Derivative of the following:

5. Find if :

6. Power Rule The table to the right gives the function and its derivative: y’ x1 x2x2 2x x3x3 3x 2 x4x4 4x 3 x -1 -1 x -2 x 1/2 x -1/2 DO YOU NOTICE ANY PATTERNS????

7. Power Rule  The derivative of is found by multiplying by the exponent n and decreasing the exponent on x by 1  If, then

8. Find the derivative: Power Rule 1. 2. 3. 4.

9. Constant times a Function If the derivative exists, the derivative of a constant times a function is the constant times the derivative of the function: y = k∙g(x) y’= k∙g’(x) Example:y = 2x 2

10. Find the Derivative: Constant times a function 1. 2. 3. 4. 5. 6.

11. Sum or Difference Rule: The derivative of a sum or difference of a function is the sum or difference of the derivatives: If f(x) = u(x) ±v(x), then f ’(x) = u’(x) ± v’(x) Example: f(x) = x 2 + 3x

12. Find the Derivative: Helpful hint: rewrite before differentiating, if possible 1. 2. 3. 4.