Copy_of_3.6_notes - c In both a and b you discovered d dx...

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Calculus Section 3.6 Page29 3.6 Chain Rule General Discussion about how functions are formed What is the difference between these functions: y = x 2 sin x y = x 2 sin x y = sin x 2 y = sin 2 x Example 1 Inside and outside functions Identify the inside and the outside function in each composition Inside Outside a) y = tan 2 x b) y = cos x 2 + 9 ( ) c) y = x 2 + 10 ( ) 15 d) y = tan sin x ( ) e) y = tan x sin x Example 2 Taking the derivative of a composition Consider the function: y = 3 x 2 + 1 ( ) 2 Determine y
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Calculus Section 3.6 Page 30 Extended Power Rule: d dx u n ( ) = Example 3 Using this Powerful Rule Determine the derivative of each function: a) y = sin 3 x b) y = 1 x 2 + 1 ( ) 3 c) y = cos x 1 + sin x 2 Example 4 Inside and Outside Function – Finding a Derivative Formula a) Plot the function Y 1 = sin X ( ) and the derivative of this function Y 2 = nDeriv Y 1 ,X,X ( ) using your graphing calculator and show the graph on the axes below:
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Calculus Section 3.6 Page31 b) Now change Y 1 = sin 2X ( ) to see the graph of the derivative of this function
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Unformatted text preview: c) In both a) and b) you discovered: d dx sin x ( ) = d dx sin 2 x ( ) = Calculus Section 3.6 Page 32 What do you think each of the following derivatives are: i) d dx cos5 x ( ) = ii) d dx sin x 2 ( ) = iii) d dx cos x 2 + 3 ( ) ( ) = iv) d dx tan 2 x − 1 ( ) ( ) = +ew Rules for Composite Trig functions: d dx sin u ( )= d dx cos u ( )= d dx tan u ( )= d dx cot u ( )= d dx sec u ( )= d dx csc u ( ) = Example 5 Using the +ew Rules and Beyond Determine dy dx for each function a) y = sin x 3 b) y = sin 3 x Calculus Section 3.6 Page33 c) y = sin cos x ( ) d) y = tan 3 x − x 2 ( ) e) y = 1 csc x + cot x f) y = x 2 sin x 2 + 3 ( ) g) y = sin x sec2 x h) y = x 2 + 6 sin 4 x i) y = x 3 3 x − 1 ( ) 4 Calculus Section 3.6 Page 34 j) y = sin 3 2 x − 1 ( ) k) y = 1 + sin 3 x ( ) 4 Assignment II–6a Page 146 – 141 #1 – 20 all...
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Copy_of_3.6_notes - c In both a and b you discovered d dx...

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