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AP Calculus I 2.4 Chain Rule St. Pius X High School Ms. Hernandez AP Calculus I F06 Q1 Derivatives Unit
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Sine and Cosine
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Product
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Quotient Lo de hi – Hi de lo
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More Trig Diff Rules
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Higher Order Derivatives First derivative y’ dy/dx Second derivative y’’ d 2 y/dx Third derivative y’’’ d 3 y/dx Fourth derivative y’’’’ d 4 y/dx y (4) …….
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f(x) = e x and f(x) = ln(x)
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Chain Rule y = f(g(x)) = f(u) y’=f’(u) u’ Outer function Inner function
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Composition Functions y=f(g(x)) y= sin2x y=tan 2 x y=(x 2 -1) 1/3 y=f(u) y=sin u y=u 2 y=u 1/3 u = g(u) u=2x u= tan x u= x 2 -1
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General Power Rule Special case of chain rule p129 f(x)=(3x-2x 2 ) 3 f’(x)=3(3x-2x 2 ) 2 (3-4x)
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Trig & Chain Rule p132 Trig function d/dx rules Parenthesis Rewriting Trig Powers
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Summary of Rules p133 Memorize them all
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2.4 Examples #15 #19 #27 #31
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#15
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#17
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#27
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#31
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