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Sladkaya [172]
3 years ago
14

Please help me I need help

Mathematics
1 answer:
vivado [14]3 years ago
3 0
What would you like me to help you with?
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If F(x) = f(x)g(x), where f and g have derivatives of all orders
user100 [1]

a. By the product rule,

F=fg\implies F'=f'g+fg'

\implies F''=(f''g+f'g')+(f'g'+fg'')=f''g+2f'g'+fg''

b. By the same rule,

F'''=(f'''g+f''g')+2(f''g'+f'g'')+(f'g''+fg''')

F'''=f'''g+3f''g'+3f'g''+fg'''

and

F^{(4)}=(f^{(4)}g+f'''g')+3(f'''g'+f''g'')+3(f''g''+f'g''')+(f'g'''+fg^{(4)})

F^{(4)}=f^{(4)}g+4f'''g'+6f''g''+4f'g'''+fg^{(4)}

c. You might recognize the coefficients as those that appear in the expansion of (a+b)^n:

1, 1

1, 2, 1

1, 3, 3, 1

1, 4, 6, 4, 1

and so on; the general pattern (known as the general Leibniz rule) is

F^{(n)}=\displaystyle\sum_{k=0}^n\binom nkf^{(n-k)}g^{(k)}

6 0
3 years ago
Please answer the question from the attachment.
NISA [10]
From what i see i think the answer is seven

3 0
3 years ago
Read 2 more answers
2x+2y=8<br> X+y=4<br> Which statement is true about the solution
laila [671]
Both x and y equal 2.

2•2=4 + 2•2=4

4+4=8

2+2=4
6 0
4 years ago
An inequality is given
alexira [117]

Answer:

  1. A
  2. A

Step-by-step explanation:

6 < 3x + 9 ≤ 18

~Subtract 9 to everything

-3 < 3x ≤ 9

~Divide 3 to everything

-1 < x < 3

I will assume the first drop down menu is the first valoue and the second drop down manu is the second value.

Best of Luck!

8 0
3 years ago
A circle has a circumference of 14pi. What is the area in terms of pi?
Elza [17]

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷The area in terms of pi is 49pi

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

5 0
3 years ago
Read 2 more answers
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