Calc math140 equivalent, Summaries of Mathematics

Math course worksheet summary walkthrough

Typology: Summaries

2023/2024

Uploaded on 02/29/2024

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Quiz4
>
derivatives
Find
the
derivatives:
I
remember
s
nx*
*
6(X)
=
8(x+h)-ox))
1)
f(x)
=
Gx2
2x2
8x
+12
3
>6(X+h)
-
2(X+h)Y
8(Xth)
H2-(6x2
-
2x4
-0x
+
12)
->
f(X)
=
6.3x2-2.4x3-8
+
3xh
+
3xh2
+
h3)
-
2/X4r4xh+
6x24xhhY)
f(x)
=
-
0x3
+
18
x
28
*
as
XY
4x3k
+
6x2n24xhthy
6/10xhoxh6h
2XY-8x3h-
1x28xh=-hYx-
8h+
-
x
+
x
+
4x2
18xh
+18xh=6h
-oxh-12xh?
Oxh-hY
8h
>
A)18x2r18xh
+
6n-8x3-12x2h-8xn2
ns
-8)
h
X
him
18x28x
8
or
->
f((X)
=
-
8x3+18x2
8
2)
f(x)
=
14
+
2x
+
3
x
2
or
3(Xth)
2+2(X+h)
HY-(3
x
2
+
2
x
+
4)
Or
->
f(X)
=
6x72
34
6X
+
34+
2x+
2n
-
2
2x
-lim
6Xr2
V
=Gxh+
3h2
2h
a416x
+
3
n
c0
>
f((X)
=
6
x
+
2
(4x3
-7x2
8]
3)
f(x)
=
6x(x
+
1)
4)
f(x)
=
(2
x
3
+
2
x
+
1)(X
=
27
~)
f(x)
=
X
=
6x6x
>
18x276
=
2x=
4x
4
+
2x24xix
=
2
f((x)
=
18x2
+
6
=2x5
-2x+X24X-2
S10X
6x72x-4
=
4x52
7X
="-8
f((X)
=
10x2
6x
4
+
2
x
-
4
*
*
X
=4x2
-
7X
-
8(X-))
6)
f(x)
=
(X
=
16)/(X
-
4)
=
6(X)
=
17)f(x)
=
ex
f(x)
=
8x-7+
2
(x+)xY).ky
a
power
rule
doesn't
apple
f((X)
=
0x3
-
7x
2
+
8
f(X)
=
eY
X
2
8)
f(x)
=
e
*
-
e
eX
(
f(x)
=
(/]
-
x(e)
-
(e
&
constant:
(number
raised
to
number)
6'(X)
=
-
ex

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Quiz4 >^ derivatives

Find the derivatives:Iremember s nx*^ * 6(X)= 8(x+h)-ox))

  1. f(x) =^ Gx22x28x +

6(X+h) -^ 2(X+h)Y8(Xth)^ H2-(6x2-^ 2x4^ -0x^ + 12) ->^ f(X)=^ 6.3x2-2.4x3-

3xh + 3xh2 + h3) - 2/X4r4xh+ 6x24xhhY)^ f(x) =^ -^ 0x3^ + 18 x 28

XY 4x3k^ as

  • 6x2n24xhthy

6/10xhoxh6h2XY-8x3h-^ 1x28xh=-hYx-8h+ - x+ x+ 4x

18xh +18xh=6h-oxh-12xh?Oxh-hY8h^ > A)18x2r18xh + 6n-8x3-12x2h-8xn2ns-8)

h (^) X

him

18x28x 8 or

-> f((X) =^ -^ 8x3+18x2^8

  1. (^) f(x) =^14 +^ 2x^ +^3 x^

or 3(Xth)^ 2+2(X+h) HY-(3 x (^2) + 2 x +

  1. (^) Or -> (^) f(X) = 6x72 (^34) 6X+ 34+ 2x+2n-^2 2x^ -lim^ 6Xr2^ V =Gxh+3h2 2h (^) a416x +

n c0^ > (^) f((X) = 6 x+ 2 (4x3-7x28]

3) f(x)^

= 6x(x+ 1)

4) f(x)^

= (2x (^3) + 2 x + 1)(X

27 ~) f(x)^ = X

= 6x6x > 18x276 = 2x=4x^4 + 2x24xix= 2 f((x) =^ 18x^

+ 6 =2x5-2x+X24X-2 S10X6x72x-4 =^ 4x52^ 7X^ ="-

f((X) = 10x26x

(^2) x - 4 *^

  • (^) X =4x2- 7X - 8(X-))

6) f(x)

(X

16)/(X - 4) = 6(X) = 17)f(x)=^ ex^ f(x) = 8x-7+ 2

(x+)xY).ky

a

power rule^ doesn'tapple

f((X) =^ 0x3-^ 7x^

(^2) + 8 f(X) = eY X 2

  1. (^) f(x) = e *- eeX

( f(x)^

= (/]

x(e)

- (e

& (^) constant: (number raised to^ number) 6'(X) =^ -^ ex