# Calc03_3 - 3.3 Differentiation Rules Colorado National...

• Notes
• 15

This preview shows pages 1–13. Sign up to view the full content.

3.3 Differentiation Rules Colorado National Monument Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2003

This preview has intentionally blurred sections. Sign up to view the full version.

If the derivative of a function is its slope, then for a constant function, the derivative must be zero. ( 29 0 d c dx = example: 3 y = 0 y = The derivative of a constant is zero.
We saw that if , . 2 y x = 2 y x = This is part of a pattern. ( 29 1 n n d x nx dx - = examples: ( 29 4 f x x = ( 29 3 4 f x x = 8 y x = 7 8 y x = power rule

This preview has intentionally blurred sections. Sign up to view the full version.

( 29 d du cu c dx dx = examples: 1 n n d cx cnx dx - = constant multiple rule: 5 4 4 7 7 5 35 d x x x dx = =
(Each term is treated separately) ( 29 d du cu c dx dx = constant multiple rule: sum and difference rules: ( 29 d du dv u v dx dx dx + = + ( 29 d du dv u v dx dx dx - = - 4 12 y x x = + 3 4 12 y x = + 4 2 2 2 y x x = - + 3 4 4 dy x x dx = -

This preview has intentionally blurred sections. Sign up to view the full version.

Example: Find the horizontal tangents of: 4 2 2 2 y x x = - + 3 4 4 dy x x dx = - Horizontal tangents occur when slope = zero. 3 4 4 0 x x - = 3 0 x x - = ( 29 2 1 0 x x - = ( 29 ( 29 1 1 0 x x x + - = 0, 1, 1 x = - Plugging the x values into the original equation, we get: 2, 1, 1 y y y = = = (The function is even , so we only get two horizontal tangents.)

This preview has intentionally blurred sections. Sign up to view the full version.

4 2 2 2 y x x = - +
4 2 2 2 y x x = - + 2 y =

This preview has intentionally blurred sections. Sign up to view the full version.

4 2 2 2 y x x = - + 2 y = 1 y =
4 2 2 2 y x x = - +

This preview has intentionally blurred sections. Sign up to view the full version.

+ 0, 1, 1 x = - 3 4 4 dy x x dx = -
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern