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The Derivatives of Composite Functions
"I can find the derivative function using the Chain Rule in function prime notation, and Leibniz notation. I can apply it in various contexts."
Function Composition
Example Given:
Find: a) b) c)
A countless number of functions, including parent functions studied, can be expressed as composite functions. Hence a derivative function for composite functions is useful.
Chain Rule
Now prove it...
Example If find in simplified/factored form.
("prime" notation)
Chain Rule("Leibniz" notation)
Example If and , find at
Example Differentiate:
Express in simplified/factored form.
(Can easily be proven)
Power of a Function Rule (an encore presentation)
Could we have differentiated the previous function after a previous lesson?
Yes! The Power of a Function Rule is a particular case of The Chain Rule:
A lot of functions....Page 105...#1f, 4e, 5ad, 6, 8c, 9a, 10, 13ad, 14, 15, 18
A3. I can verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems;