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3 years ago

Plz plz, help I don't understand 24 points !!! Will mark brainiest for correct answers only quick!!!

Mathematics

1 answer:

olya-2409 [2.1K]3 years ago

6 0

The triangle is kinda square so multiply and you should get 24

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a. By the product rule,

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

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

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

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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

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

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<h3>Answer: a^2 - b^2 = (a-b)(a+b)</h3>

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