PowerPoint presentation in Basic calculus

1.  

2. At the end of the lesson, the students are
expected to:
 Illustrate the Chain Rule of
Differentiation. (STEM_BC11D-IIIh-
2)
Solve problems using the Chain Rule.
(STEM_BC11D-IIIh-2)

4. Directions:
Each group will pick a question and will
discuss among themselves on how you
can solve the given activity . You will
write your answer in the cartolina and
will explain it in a “creative way” just
like rapping, role playing, etc.

5.  Find of the functions:
1.
2.
3.

6. 1.
2.
3.
4
)
8
3
(
)
1
12
(
3
4
3





x
x
x
dx
dy
3 2
)
1
2
(
3
2


x
dx
dy
7
4
3
)
1
(
24
x
x
dx
dy



7.  How did you find the activity?
 What difficulties have you encountered in the
activity?
 What mathematical concepts did you use in solving
the given?
 What conclusion can you derive from your
observation in our activity?

8. CHAIN RULE
It is a special rule,
exists for differentiating
a function of another
function, which is the
same as composite

9. y = f(g(x))
Let u = f(u)
Then y = f(u)
And
)
)(
(
dx
du
du
dy
dx
dy


10.  He was a German
polymath and philosopher
born on July 1, 1646.
He occupied a
prominent place in the
history of mathematics
and philosophy having
developed “differential
and integral calculus”
independently of Isaac

11. Find the derivative of the function
Solution:
Let
3
4
)
8
3
( 

 x
x
y
8
3 4


 x
x
u
1
12 3

 x
dx
du
3

 u
y
4
3 

 u
du
dy

12. )
)(
(
dx
du
du
dy
dx
dy

)
1
12
)(
3
( 3
4


 
x
u
)
1
12
(
)
8
3
(
3 3
4
4




 
x
x
x
4
)
8
3
(
)
1
12
(
3
4
3





x
x
x

13. 3
1
2 
 x
y
Find the derivative of
the function
Solution:
Let
)
1
2
( 
 x
u
2

dx
du
3
/
1
x
u 
3
2
3
1 
 u
du
dy
)
)(
(
dx
du
du
dy
dx
dy

)
2
(
3
1 3
2

 u
3 2
)
1
2
(
3
2


x

14. 6
)
4
(
1


x
y
Find the derivative of
the function
Solution:
Let
4
1 x
u 

3
4x
dx
du


6

 u
y
7
6


 u
dx
du
)
)(
(
dx
du
du
dy
dx
dy

)
4
)(
6
( 3
7
x
u 

 
)
4
(
)
1
(
6 3
7
4
x
x 


 
7
4
3
)
1
(
24
x
x



15. Find the derivative of
the function
(Individual)
On ½ sheet of pad paper:
.
7
2

 x
y
Answer:
1

dx
dy
(By Group)
Create your
own
equation/function
by applying the
chain rule of
differentiation.
Write the
solution in the

18. Go out of your way to
show compassion. It will
start a “CHAIN” reaction
and you’ll never know
how far a little kindness
can go.

19. 

