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Unformatted text preview: n x u y )] ( [ = Examples: ( 29 3 3 2 3 8 ) 7 9 ( += + = x y t y What about Trig functions and Exponentials? dx du e e dx d dx du u u dx d dx du u u dx d dx du u u dx d u u ) ( ] [ tan) (sec ] [sec ) (sec ] [tan ) (cos ] [sin 2 = = = = dx du u u u dx d dx du u u dx d dx du u u dx d ) cot (csc ] [csc ) (csc ] [cot ) (sin ] [cos 2=== Examples x y x x y 3 tan 2 sin sin = + = Exponentials and Logarithms Let a be a positive real number not = 1 and let u be a differentiable function of x. , 1 ] [ln = u dx du y u dx d dx du u u dx d 1 ] [ln = , 1 ] [ln = x x x dx d [ ] [ ] dx du a a a dx d a a a dx d u u x x ) )( (ln ) )( (ln = = [ ] [ ] dx du u a u dx d x a x dx d a a ) (ln 1 log ) (ln 1 log = = More Examples: x y x y x y 3 3 3 6 sec ) 2 ln( = = + = And more examples The chain rule can be used in conjunction with both product and quotient rules. You will need to decide what you should do first. ( 29 2 5 2 ) ( 2 5 2 ) ( 2 5 5 2 + + = + + = x x x g x x x g...
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 Spring '11
 PamelaSatterfield
 Chain Rule, Derivative, The Chain Rule

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