9.5 First Derivatives of Composite Function

(A) Differentiate Composite Function using Chain Rule


Example:
Differentiate y = (x2– 1)8 .

Solution:


(B) Differentiate Composite Function using Alternative Method
       – Easy Version

Example:
Differentiate y = (x2 – 1)8 .

Solution:
y = ( x 2 1 ) 8 d y d x = 8 ( x 2 1 ) 7 d d x ( x 2 1 ) d y d x = 8 ( x 2 1 ) 7 ( 2 x ) d y d x = 16 x ( x 2 1 ) 7

Practice 1:
Given that  y = 1 3 x 7 ,  find  d y d x
Solution:
y = 1 3 x 7 = ( 3 x 7 ) 1 d y d x = 1 ( 3 x 7 ) 2 .3 d y d x = 3 ( 3 x 7 ) 2


Practice 2:
Given that  y = 2 x 2 5 x + 1 ,  find  d y d x
Solution:
y = 2 x 2 5 x + 1 = ( 2 x 2 5 x + 1 ) 1 2 d y d x = 1 2 ( 2 x 2 5 x + 1 ) 1 2 ( 4 x 5 ) d y d x = 4 x 5 2 2 x 2 5 x + 1

Leave a Reply

Your email address will not be published. Required fields are marked *