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CIE A Level Maths: Pure 1复习笔记5.1.2 Definition of Derivatives
Category:
A-level课程
,
教材笔记
,
福利干货
Date: 2022年8月19日 上午11:08
Definition of Derivatives
What is the derivative of a function?
Differentiation
is an operation that calculates the
rate of change
of a
function
with respect to a variable
This means how much the function varies when the variable increases by one unit
To
differentiate
a function (f(
x
)) with respect to the variable
x
we use the
notation
The result is called the
derivative
What is the link between derivatives and gradients?
The rate of change of a function f(
x
) with respect to
x
can be thought of as the
gradient
function
of the graph
y
= f(
x
)
We can write the gradient function (or derivative) as
For the
quadratic function
f(
x
) =
x
² the gradient varies
Near the origin the gradient is close to 0
As
x
increases the gradient of the graph increases
How can I find the derivative of a function at a point?
The
derivative
of a function (or gradient of its graph) at a point is equal to the
gradient of the tangent
to the graph at that point
To
estimate
the gradient you could
draw the tangent
and calculate its
gradient
To find the
actual gradient
at a point
x
Pick a
second point
on the curve close to the first point (call it
x
+
h
)
Calculate the
gradient of the chord
joining the two points
You do
not
need to remember this formula
Worked Example
Exam Tip
Deriving a derivative from scratch is
not examinable
This revision note is intended to give you an understanding of what derivatives do
转载自savemyexams
Previous post: CIE A Level Maths: Pure 1复习笔记5.1.1 Definition of Gradient
Next post: CIE A Level Maths: Pure 1复习笔记5.1.3 Differentiating Powers of x
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