05Techniques of DifferentiationIII

05Techniques of DifferentiationIII - ( x F if 3 2 ) ( 2 + =...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
T ECHNIQUES OF D IFFERENTIATION – T HE C HAIN R ULE There is another technique to differentiate the composition of two functions. This is called the Chain Rule . If ) ( x g and )) ( ( x g f both exist, and g f F = is the composite function defined by )), ( ( ) ( x g f x F = then ) ( x F exists and is given by ) ( )) ( ( ) ( x g x g f x F = , or In Leibniz notation, if ) ( x f y = and ) ( x g y = are both differentiable functions, then dx dy dy dy dx dy = . Ex . Differentiate 1 ) ( 2 + = x x F . Ex . If 1 2 3 + + = u u y , where 1 2 2 - = x u , find 2 = x dx dy “the derivative at x = 2”. Ex . Find )
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( x F if 3 2 ) ( 2 + = x x F . Special Case: Power Rule combined with Chain Rule If n is any real number and ) ( x g u = is differentiable, then dx dy nu u dx d n n 1 ) (-= or, [ ] [ ] ) ( ) ( ) ( 1 x g x g n x g dx d n n =-. Ex . If 8 2 ) 2 ( +-= x x y , find dx dy . Ex . Differentiate 100 3 ) 1 (-= x y . Assign: p.209 #7-13, 35-39, 49, 50, Worksheet no implicit differentiation...
View Full Document

Page1 / 2

05Techniques of DifferentiationIII - ( x F if 3 2 ) ( 2 + =...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online