- The document discusses product and quotient rules for finding derivatives of functions. - The product rule states that the derivative of two functions multiplied together (f(x) = u(x)v(x)) is the first function multiplied by the derivative of the second plus the second function multiplied by the derivative of the first. - The quotient rule is provided but not explained for finding the derivative of a function that is a quotient of two other functions.

1. Find if: y = 2 x3
sinx

2. Product and quotient rules
By the end of the lesson you will be able to:
• Use the product and quotient rules to find the
derivative of functions.

3. If f (x) = u(x). v(x) then
f '(x)= u'(x).v(x)+u(x).v'(x)
simpler: (uv)' = u'v+uv'
The product rule

4. Find if: y = 2 x3
sin x

5. Find if:

6. Find if:

7. Find if:

8. Find if:

9. Find for y= ex
sin x

10. The quotient rule
If then:
simpler:
2

11. Find if:

12. Find if:

13. Find if:

14. Find if:

15. Differentiate with respect to x:

16. Find if:

17. Find if:

18. Find the equations of the tangent line to the curve
y= x cos x at the point where x = π.

19. The function has a
horizontal tangent line at x = k. Find k.

20. Find the coordinates of the two points on the curve
y= sinx ( 2 cos x+1), in the range
where the gradient is

21. Find the coordinates of the stationary points on the
curve in the range 0≤x≤2π.

22. Find and classify the stationary points on the curve
y= x2
ex
. Hence sketch the curve.

23. Solve book Page 220 Ex 7C