CAIE A-Level Mathematics A2 3.4.3 Differentiation Rules Questions

State or imply 6 y^2 d y/ d x as the derivative of 2 y^3
State or imply 3 x^2 d y/ d x+6 x y as the derivative of 3 x^2 y
Complete the differentiation and equate the derivative of the LHS to zero and
solve for d y/ d x (the =0 can be implied)
Needs to be clear how the value of d y/ d x was obtained,
e.g. collecting like terms and using brackets.

Obtain d y/ d x=x^2+2 x y2 y^2-x^2 from correct working
AG

Marking guidance:

Accept d y/ d x=2 x y+x^22 y^2-x^2.

No incorrect statements, e.g. 'cancel by 3 ' or 'divide top and bottom by 3 ' are acceptable, but to have d y/ d x=3 x^2+6 x y6 y^2-3 x^2 and say "divide by 3 " at the final step scores A0.

Equate derivative to 0 and solve for x or for x in terms of y.

*M1

E.g., x^2+2 x y=0 x=0 or x=-2 y.
Must be using the numerator.

Obtain (0,2)
Marking guidance:

Allow if the values are stated separately.
Do not ISW.

Use their x=-2 y to form an equation in one unknown
Or equivalent e.g. substitute y=-x^22 x
E.g., 2 y^3-12 y^3+8 y^3=16 or
-2(1/8 x^3)+3(1/2 x^3)-x^3=16.

Obtain (4, - 2)
Allow if the values are stated separately.
Do not ISW