(A) Differentiate Composite Function using Chain Rule
Example:
Example:
Example:
Differentiate y = (x2– 1)8 .
Solution:
(B) Differentiate Composite Function using Alternative Method
- Easy Version
- Easy Version
Differentiate y = (x2 – 1)8 .
Solution:
y=(x2−1)8dydx=8(x2−1)7ddx(x2−1)dydx=8(x2−1)7(2x)dydx=16x(x2−1)7
Practice 1:
Given that y=13x−7, find dydx
Solution:
y=13x−7=(3x−7)−1dydx=−1(3x−7)−2.3dydx=−3(3x−7)2
Given that y=13x−7, find dydx
Solution:
y=13x−7=(3x−7)−1dydx=−1(3x−7)−2.3dydx=−3(3x−7)2
Practice 2:
Given that y=√2x2−5x+1, find dydx
Solution:
y=√2x2−5x+1=(2x2−5x+1)12dydx=12(2x2−5x+1)−12(4x−5)dydx=4x−52√2x2−5x+1
Given that y=√2x2−5x+1, find dydx
Solution:
y=√2x2−5x+1=(2x2−5x+1)12dydx=12(2x2−5x+1)−12(4x−5)dydx=4x−52√2x2−5x+1