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=(x21)8dydx=8(x21)7ddx(x21)dydx=8(x21)7(2x)dydx=16x(x21)7


Practice 1:
Given that y=13x7, find dydx

Solution:
y=13x7=(3x7)1dydx=1(3x7)2.3dydx=3(3x7)2


Practice 2:
Given that y=2x25x+1, find dydx

Solution:
y=2x25x+1=(2x25x+1)12dydx=12(2x25x+1)12(4x5)dydx=4x522x25x+1