1 / 18

Section 2.4 – The Chain Rule

Section 2.4 – The Chain Rule. Warm-Up. Wrong answer: The exponent of 30. Although the exponent makes the derivative difficult, we could use the product rule to find the derivative. Right answer: The function inside of the secant function.

yuri
Download Presentation

Section 2.4 – The Chain Rule

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 2.4 – The Chain Rule

  2. Warm-Up Wrong answer: The exponent of 30. Although the exponent makes the derivative difficult, we could use the product rule to find the derivative. Right answer: The function inside of the secant function. We have not taken the derivative of a composition of functions. Explain why we can not differentiate the function below:

  3. Composition of Functions COMPOSITION OF FUNCTIONS If and , find .

  4. Decomposition of Functions If each function below represents , define and . DECOMPOSITION OF FUNCTIONS

  5. The Chain Rule Other ways to write the Rule: If y = f(u)is a differentiable function of u and u = g(x)is a differentiable function of x, then y = f(g(x)) is a differentiable function of x, and

  6. Instructions for The Chain Rule Make sure each function can be differentiated. For , to find : • Decompose the function • Differentiate the MOTHER FUNCTION • Differentiate the COMPOSED FUNCTION • Multiply the resultant derivatives • Substitute for u and Simplify

  7. Example 1 Define f and u: Find the derivative of f and u: Use the Chain Rule: Substitute: Substitute for u: Simplify: Find if and .

  8. Example 2 Define f and u: Find the derivative of f and u: Use the Chain Rule: Substitute: Substitute for u: Simplify: Differentiate .

  9. Example 3 Define h and u: Find the derivative of h and u: If f and g are differentiable, , , and ; find .

  10. Example 4 Define f and u: Find the derivative of f and u: Find if .

  11. White Board Challege Find f '(-2) if:

  12. Example 5 Define f and u: Find the derivative of f and u: OR Differentiate .

  13. Example 6 Use the old derivative rules Chain Rule Twice Differentiate .

  14. Example 7 Quotient Rule Chain Rule Find the derivative of the function .

  15. Example 8 Product Rule Chain Rule Twice Differentiate .

  16. White Board Challege Find the equation of the tangent to the curve y=3sin(2x) at the point:

  17. Example 9 Chain Rule Chain Rule Again Differentiate .

  18. Example 10 Find the Derivative Evaluate the Derivative at x = π Find the equation of the line Find an equation of the tangent line to at .

More Related