3x 2 a f x cose b g x csc x c

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Unformatted text preview: ue
of
the

 The
slope
of
a
tangent
line
to
the
curve
 func0on
at
that
point.
 













is
equal
to
the
value
of
the

 func0on
at
that
point.
 € x Deriva0ves
of
Exponen0al
Func0ons
 f ( x) = a , If


















then
 f ' ( x ) = a ⋅ ln a. x x Example:
 € Differen0ate.
 x g( x ) = 7 x + x 7 




(c)
 h ( x ) 
= 2
5 x +
1
 (a)  


(
x ) 
= e 
 


(b) 
 
 
 
 
 
 f 2 € € € Deriva0ves
of
Logarithmic
Func0ons
 1 . f ( x ) = log a x, If


























then
 f ' ( x ) = x ⋅ ln a Example
1:

 Differen0ate.
 (a)
 f (
x ) = ln
 x 
 
(b)
 g( x ) = log 4 ( x 2 + 5 x + 6) 
€ Example
2:
 Determine
the
equa0on
of
the
tangent
line
to
the
 €x ln curve























at
the
point

 P (1, 0). f ( x) = 
 
 



 x € € € Deriva0ves
of
Trigonometric
Func0ons
 2 y = sin x y = sin x 1 
 
 
 
 -5 
 -4 -3 

 -2 -1 0 1 2 3 4 5 € € -1 -2 2 y = cos x 1 -5 -4 -3 -2 -1 0 1 2 € -1 -2...
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This note was uploaded on 03/03/2014 for the course MATH 1LS3 taught by Professor Lovric during the Winter '09 term at McMaster University.

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