Derivatives Unit I Cram Guide
Limit Definition of Differentiability
a Derivative ·
The function must be continuous at
-(a)
f'(a) m+
h) the point
+ -
=
Alternative Form of 0 The left-hand derivative and right-
hand derivative must be equal
theLimit Dinin,
Derivative Rules
Average Rates of
. Power Rule :
1 Change
AROC =
1
f(x) x f'(x) nxn
-
= =
. Constant Rule
2 :
~
position function s(t)
at
f(x) f'(x) 0
-
describes the location
= 1 =
time t
3
. Constant Multiple Rule :
function -(t)
-
velocity
f(x) cog(x) t'(x) cog'(x)
-
= = = is rate of change with
to time
4 Sum/Difference Rule : respect
· coving foraand
.
f(x) =
g(x) = h(x) f(x) g(x) = h'(x) =
Acceleration function act)
5. Product Rule
-
change with respect
-
is rate of
f(x) g(x)h(x) = j(x)
-
=
g(x)h(x) g(x)h(x)
+
to time
6. Quotient Rule
nl
f(x) =- f(x) = x)gXg() 1
logarithms
.
log(xy) logy(x) log(y)
= +
Tangent Lines 2
109p( * ) logy(x) logy(y)
= -
y - f(a) )(a)(X a)
.
= -
3 logy(x) nlogp(x)
=
. Find the derivative f'(x)
4
.
. Evaluate f(a) to find the
2
4 .
109() = a
slope
3 Use thePoint .
(a
,
f(a)
and theslopef(a) in
the print-slope formula
Limit Definition of Differentiability
a Derivative ·
The function must be continuous at
-(a)
f'(a) m+
h) the point
+ -
=
Alternative Form of 0 The left-hand derivative and right-
hand derivative must be equal
theLimit Dinin,
Derivative Rules
Average Rates of
. Power Rule :
1 Change
AROC =
1
f(x) x f'(x) nxn
-
= =
. Constant Rule
2 :
~
position function s(t)
at
f(x) f'(x) 0
-
describes the location
= 1 =
time t
3
. Constant Multiple Rule :
function -(t)
-
velocity
f(x) cog(x) t'(x) cog'(x)
-
= = = is rate of change with
to time
4 Sum/Difference Rule : respect
· coving foraand
.
f(x) =
g(x) = h(x) f(x) g(x) = h'(x) =
Acceleration function act)
5. Product Rule
-
change with respect
-
is rate of
f(x) g(x)h(x) = j(x)
-
=
g(x)h(x) g(x)h(x)
+
to time
6. Quotient Rule
nl
f(x) =- f(x) = x)gXg() 1
logarithms
.
log(xy) logy(x) log(y)
= +
Tangent Lines 2
109p( * ) logy(x) logy(y)
= -
y - f(a) )(a)(X a)
.
= -
3 logy(x) nlogp(x)
=
. Find the derivative f'(x)
4
.
. Evaluate f(a) to find the
2
4 .
109() = a
slope
3 Use thePoint .
(a
,
f(a)
and theslopef(a) in
the print-slope formula
