Before the midterm

Getting the sign of a trigonometric derivative wrong

The habit: The derivative of cos is minus sin; check the sign before anything else.

22 practice questions are built to catch it, in 7 topics.

Practise against it: 6 questions

What it looks like

A question from exponential and trigonometric functions, with the answer this slip gives beside the right one.

Introductory1 mark · 2 min

Let $f(x) = 4e^{x} - 2\sin x$ . Find $f'(0)$ .

With the slip: $\displaystyle 6$
Worked through: $\displaystyle f'(0) = 2$

(sin x)′ = cos x, with no minus, so the −2 sin x term contributes −2 cos 0 to f′(0): it lowers f′(0) rather than raising it.

See the worked solution

Where it comes up

Exponential and trigonometric functions9 questions
The chain rule and logarithms3 questions
Implicit differentiation and inverse trigonometric functions5 questions
L’Hôpital’s rule1 question
Taylor polynomials1 question
Newton’s method1 question
Antiderivatives2 questions

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
Let $f(x) = 3\tan x - 2\sec x$ . Find $f'\!\left(\dfrac{\pi}{6}\right)$ .
Exponential and trigonometric functionsIntroductory
02
Let $f(x) = \cot x + \csc x$ for $0 < x < \pi$ . Find $f'(x)$ .
Exponential and trigonometric functionsIntroductory
03
A student finds $y'\!\left(\tfrac{\pi}{2}\right)$ for the function below as shown. Find the first line that is wrong. $\displaystyle y = x\cos x$
Exponential and trigonometric functionsStandard
04
Each working below writes $\tan x = \dfrac{\sin x}{\cos x}$ and differentiates it. Which one is correct at every step?
Exponential and trigonometric functionsStandard
05
Let $f(x) = \dfrac{e^{x}}{2 + \cos x}$ . Find $f'\!\left(\dfrac{\pi}{2}\right)$ .
Exponential and trigonometric functionsStandard
06
Let $f(x) = e^{x}(\sin x - \cos x)$ . Find $f'(x)$ .
Exponential and trigonometric functionsStandard