Derivatives

"But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not"

Johann Bernoulli

Derivatives of known Functions

What you have to know:

Recognize all the basic functions
You must be able to expand and factorise the square difference and perfect square expressions.
(If not, check this lesson)
You must be able to manipulate exponential expressions.
(If not, check this lesson)
You must be able to manipulate logarithmic expressions.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Check out this presentation.

Geometric explanation of Derivatives

What you have to know:

How to calculate Area

Key Points

1. Watch the video:

Extra

Material and references:

Hodder Book SL(ISBN: 9781510462359) :
9A, 9B, 9C, 20A

Key Points

You should be able to differentiate functions such as
\( \sqrt{x} \), \( \sin x \) and \( \ln x \).
If \( f(x) = x^n \), where \( n \in \mathbb{Q} \), then
\( f'(x) = nx^{n-1} \);
if \( f(x) = \sin x \), then \( f'(x) = \cos x \);
if \( f(x) = \cos x \), then \( f'(x) = -\sin x \);
if \( f(x) = e^x \), then \( f'(x) = e^x \); and
if \( f(x) = \ln x \), then \( f'(x) = \frac{1}{x} \).

IB Past Paper Problems

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