Before the final

Misreading where a power sits

The habit: sin(x²) and (sin x)² are different functions; read the brackets before differentiating.

12 practice questions are built to catch it, in 6 topics.

Practise against it: 6 questions

What it looks like

A question from Taylor polynomials, with the answer this slip gives beside the right one.

Introductory2 marks · 3 min

Find the coefficient of $x^{3}$ in the third-order Maclaurin polynomial of $f(x) = \log(1 + 2x)$ .

With the slip: $\displaystyle \approx 0.6667$
Worked through: $\displaystyle \frac{8}{3}$

2x³/3 leaves the 2 uncubed. The cube in (2x)³/3 applies to the 2 as well as the x.

See the worked solution

Where it comes up

Limits1 question
The definition of the derivative1 question
The chain rule and logarithms2 questions
Implicit differentiation and inverse trigonometric functions2 questions
Taylor polynomials5 questions
Exponential growth and decay1 question

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

01
Which limit represents $g'(9)$ for $g(x) = \sqrt{x}$ ?
The definition of the derivativeIntroductory
02
Let $F(x) = \sin\!\left(x^{2}\right)$ . Which of the following is $F'(x)$ ?
The chain rule and logarithmsIntroductory
03
Let $f(x) = \tan^{3}x$ for $-\tfrac{\pi}{2} < x < \tfrac{\pi}{2}$ . Find $f'(x)$ .
The chain rule and logarithmsIntroductory
04
In implicit differentiation, $y$ stands for an unknown function of $x$ . Which expression equals $\dfrac{d}{dx}\bigl(y^{3}\bigr)$ ?
Implicit differentiation and inverse trigonometric functionsIntroductory
05
Let $f(x) = \arctan(3x)$ . Find $f'(x)$ .
Implicit differentiation and inverse trigonometric functionsIntroductory
06
Evaluate the limit. $\displaystyle \lim_{x \to 0} \frac{1 - \cos^{2}(3x)}{4x^{2}}$
LimitsStandard