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Calculus_2
Also remember that there are other ways of representing derivatives are as follows:
;
Now we can also find derivatives using rules. This means that if
the question does not “force you”
to use the “long method” then
you can work out the derivatives
using the following rules.
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1. The derivative of a constant is 0.
Example:
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2. If f(x) is a power, i.e.
NOTE: n is any real no.
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Example
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3. If a constant, k is
multiplied by f(x).i.e.
Example
NOTE the following important rules:
1. Convert fractions that have
exponents in the base as follows:
OR
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2. Convert surds to powers by
remembering the ffg rule:
.
Example:
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APPLICATION EXAMPLES
1.
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2.
(First remove brackets and simplify)
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3.
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4.
ALWAYS simplify FIRST:
Now find f’(x)
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ANOTHER EXAMPLE
1. Find the equation of the
tangent to the graph of
at the point(1;2)
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SOLUTION
STEP 1
Find the derivative (gradient):
STEP 2
Now substitute x=1,
to get the value of the
gradient at this point.
STEP 3
Since a tangent is a straight line,
it will have the form y=mx+c
Note that m = the gradient
STEP 4
Now we have the find the
value of “c”. To do this we
substitute the given point
(1;2) and then solve for c.
2=8(1)+ c
2=8+c
2-8=c
-6 = c
So: y=8x-6