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# Chapter 2(B) - Other Types of Differentiation Cartesian...

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Other Types of Differentiation

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3 4 y xx =+ 2 y Cartesian equation --- An equation connecting and xy Parametric equations 2 1. 2 1 xt yt = 2. si n 2 co s5 qq = + =- 22 9 += 2 3. 1 tt x e ye =
Other Types of Differentiation n Parametric Differentiation we have ) ( ' ) ( ' t v t u dt dx dt dy dx dy = = = = = ), ( ) ( where ), ( Given t v x t u y x f y

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Parametric Differentiation - Example n Let ( si n ) and ( 1 co s ). Find . dy x a tt y at dx = - =- = = - = 2 cot 2 sin 2 2 cos 2 sin 2 ) cos 1 ( sin 2 t t t t t a t a dx dy
) ( ' ) ( ' t v t u dt dx dt dy dx dy = = ( ) ( ) x v t y ut == Pause and Think !!! True or false ?? 2 2 2 2 2 2 ''( ) dy d y dt dx d x vt dt

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Derivative – Rules of Differentiation d y d y du d x d u dx =⋅ Chain Rule d dx ( ) () yy d du du dx
3 4 y xx =+ 2 y Cartesian equation --- An equation connecting and xy 22 9 += 2 34 dy x dx 1 2 2 dy x dx x Use Implicit Differentiation

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Ordinary differentiation Implicit differentiation 2 ()2 d xx dx = 1 () nn d x nx dx - = (si n) cos d dx = 1 (l d x d = d ee dx = ( )1 d x dx = 2 d dy yy d x dx = 1 d dy y ny d x dx - = (si cos d dy d x dx = 1 (l d dy y d x y dx = d dy d x dx = ()1 d dy y d x dx =
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Chapter 2(B) - Other Types of Differentiation Cartesian...

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