Calculas Chain rule
+
Quotient Rule
introduction Quotient
Chain Rule
-
Rule
i e
Formula :
3x Nur
.
f(x) = + 2x
fi
C
:
f'(x) = 6x + 2
ie
.
(4x" -
3x2)(2x3 -
4x)
Chain Rule eliminates the indicies
, u = (4x -
3x) v = (2x 4x") -
& multiplies the bases u = 8x - 6x v = bx - 8x
In the example :
using the formula sub the
3
,
f(x) = + 2x values back into the equation
original
orig ina11
3x2)(6x 8 2)
1
subtracted
4x))2x3 4x) (4x'
the power ,
181
h is ,
+
-
(x)
-
-
=
by 1
,
then multiplied by
the base (6x2 8()2
-
.
S E f(x)
I
= 3x + 2x
= 16x"
-
-
32x3 -
12x" + 24, 24x" -
+
32x3 18x"
-
+ 24x
&
is -
2 -
1
f'(x) 3x2x 2x
(6x2 8()2
=
+
-
[
2 =
=
x
xx
+
+
~
2x)x
4x" 8x3 - 32x" + 56x3
= -
-
w ~
28x4 46x3
=
+
Simplify If necessary
-
1 -
1 = 0
anything to the
#for asked
-
(6x" 8x)2
1 Therefore the
power of O
, equals .
, -
2
is removed , leaving 2 .
always leave
+
Quotient Rule
introduction Quotient
Chain Rule
-
Rule
i e
Formula :
3x Nur
.
f(x) = + 2x
fi
C
:
f'(x) = 6x + 2
ie
.
(4x" -
3x2)(2x3 -
4x)
Chain Rule eliminates the indicies
, u = (4x -
3x) v = (2x 4x") -
& multiplies the bases u = 8x - 6x v = bx - 8x
In the example :
using the formula sub the
3
,
f(x) = + 2x values back into the equation
original
orig ina11
3x2)(6x 8 2)
1
subtracted
4x))2x3 4x) (4x'
the power ,
181
h is ,
+
-
(x)
-
-
=
by 1
,
then multiplied by
the base (6x2 8()2
-
.
S E f(x)
I
= 3x + 2x
= 16x"
-
-
32x3 -
12x" + 24, 24x" -
+
32x3 18x"
-
+ 24x
&
is -
2 -
1
f'(x) 3x2x 2x
(6x2 8()2
=
+
-
[
2 =
=
x
xx
+
+
~
2x)x
4x" 8x3 - 32x" + 56x3
= -
-
w ~
28x4 46x3
=
+
Simplify If necessary
-
1 -
1 = 0
anything to the
#for asked
-
(6x" 8x)2
1 Therefore the
power of O
, equals .
, -
2
is removed , leaving 2 .
always leave
