Presentation is loading. Please wait.

Presentation is loading. Please wait.

Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve.

Similar presentations


Presentation on theme: "Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve."— Presentation transcript:

1 Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve.

2 We can do the same thing for slope The resulting curve is a sine curve that has been reflected about the x-axis.

3 Derivative of y=sinx Use the definition of the derivative To prove the derivative of y=sinx is y’=cosx.

4 Derivative of y=sinx Shortcut: y’=cosx The proof of the d(cosx) = -sinx is almost identical

5

6 product rule: Notice that this is not just the product of two derivatives. This is sometimes memorized as:

7 Example:

8

9

10 Try this:

11

12

13

14

15

16 quotient rule: or

17 Quotient Rule

18

19

20

21


Download ppt "Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve."

Similar presentations


Ads by Google