The document discusses applying the chain rule to find derivatives of composite functions. It provides examples of identifying composite functions and using the chain rule formula to take derivatives. It lists practice problems for students to find derivatives of various composite functions using the chain rule, including functions with exponents like (x3 + 1)8, as well as trigonometric functions like y = sin(4x).

1. Find and classify the stationary points on the curve
y= x2
ex
.

2. We need a rule to simplify these cases.
Find the derivative of x3
+1 :
Find the derivative of (x3
+1)2
:
x6
+2x3
+1we need to expand first:
3x2
6x5
+6x
6x2
(x3
+1)
But, what if we have to find the derivative of (x3
+1)8
?
We need a rule to simplify these cases.

3. The chain rule
By the end of the lesson you will be able to:
• Find the derivative of composite functions by
applying the chain rule.

4. The following functions are a composition of other
two simpler functions. Can you identify them?
and
as in:

5. The expression y = ( x3
+1)2
is a composition of
two simpler functions :
y= u2
and u= x3
+1
f(x) = x2
and g(x)= x3
+1
f(g(x))= (x3
+1)2
or

6. The chain rule says :
y = f(u) ⇒

7. In the example: y = (x3
+1)2
y =u2
and u = x3
+1

8. Find if y = (3x­1)7
:

9. Find if y = 5(1­x)3
:

10. Find if

11. Find if

12. Find if y =(x2
+1)100

13. Find the derivative of y = sin (4x)

16. Find if

20. Find where the tangent to
cuts the x­axis.
at x =0

21. Consider the function for
What is the domain of f ?
Find and hence find intervals where f(x)
is increasing.

22. A body moves along the x­axis with displacement
function
where t is the time in seconds,
Find the velocity and acceleration functions for
the motion of the body.

23. Solve Book: page 212 Ex 7A : at least
5 exercises of each question.

24. http://www.maths­bingo.com/DifferentiationChainRule.html
At the end of the lesson: