SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Calculus, MET1 2018 VCAA 1a

If  `y = (−3x^3 + x^2 - 64)^3`, find  `(dy)/(dx)`.  (1 mark)

Show Answers Only

`3(−3x^3 + x^2 – 64)^2 · (−9x^2 + 2x)`

Show Worked Solution

Mean mark 58%!
MARKER’S COMMENT: Poor use use brackets was notable.

`y` `= (−3x^3 + x^2 – 64)^3`
`(dy)/(dx)` `= 3(−3x^3 + x^2 – 64)^2 · (−9x^2 + 2x)`

 

Calculus, MET2 2009 VCAA 15 MC

For  `y = sqrt (1 - f(x)),\ \ (dy)/(dx)`  is equal to

A.   `(2 f prime (x))/(sqrt(1 - f(x))`

B.   `(-1)/(2 sqrt (1 - f prime (x)))`

C.   `1/2 sqrt (1 - f prime (x))`

D.   `3/(2(1 - f prime(x)))`

E.   `(-f prime (x))/(2 sqrt (1 - f (x)))`

Show Answers Only

`E`

Show Worked Solution

`text(Using Chain Rule,)`

`dy/dx` `= – f′(x) xx 1/2 xx (1-f(x))^(- 1/2)`
  `=(- f′(x))/(2 sqrt (1 – f (x)))`

`=>   E`

Calculus, MET1 2011 VCAA 1a

Differentiate  `sqrt (4 - x)`  with respect to `x.`  (1 mark)

Show Answers Only

`(dy)/(dx) = (– 1)/(2 sqrt (4 – x))`

Show Worked Solution

`text(Using the Chain Rule:)`

`text(Let)\ \ y` `= (4 – x)^(1/2)`
`:. (dy)/(dx)` `= 1/2 (4 – x)^(-1/2) (- 1)`
  `= (– 1)/(2 sqrt (4 – x))`