{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lesson 4-filled2

# Lesson 4-filled2 - x f dx d x g x f dx d ± = ± Example 7...

This preview shows pages 1–5. Sign up to view the full content.

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

View Full Document
Math 1314 Lesson 4 Basic Rules of Differentiation We can use the limit definition of the derivative to find the derivative of every function, but it isn’t always convenient. Fortunately, there are some rules for finding derivatives which will make this easier. First, a bit of notation: [ ] ) ( x f dx d is a notation that means “the derivative of f with respect to x , evaluated at x .” Rule 1: The Derivative of a Constant [ ] , 0 = c dx d where c is a constant. Example 1 : If , 17 ) ( - = x f find ) ( ' x f . Rule 2: The Power Rule [ ] 1 - = n n nx x dx d for any real number n Example 2 : If , ) ( 5 x x f = find ) ( ' x f . Example 3 : If x x f = ) ( , find ) ( ' x f .
Example 4 : If , 1 ) ( 3 x x f = find ) ( ' x f . Rule 3: Derivative of a Constant Multiple of a Function [ ] [ ] ) ( ) ( x f dx d c x cf dx d = where c is any real number Example 5 : If , 3 ) ( 4 x x f - = find ) ( ' x f . Example 6 : If , 5 ) ( 3 x x f = find ) ( ' x f . Rule 4: The Sum/Difference Rule [ ] [ ] [ ] ) ( ) ( ) ( ) ( x g dx d x f dx

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x f dx d x g x f dx d ± = ± Example 7 : Find the derivative: . 7 4 2 4 ) ( 2 3 x x x x f +--= Rule 5: The Derivative of the Exponential Function [ ] x x e e dx d = Example 8 : Find the derivative: x e x x x f 6 2 4 ) ( 3 +-+ = Rule 6: The Derivative of an Exponential Function (base is not e ) [ ] ( 29 x x a a a dx d ⋅ = ln Example 9: Find the derivative: x x f 4 ) ( = Rule 7: The Derivative of the Logarithmic Function [ ] x x dx d 1 | | ln = , provided ≠ x Example 10 : Find the derivative: ) ln( 6 2 5 ) ( x x x f +--= From this lesson, you should be able to State the basic rules for finding derivatives Select the appropriate rule to use for a given problem Find the derivative of a function using the basic rules...
View Full 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