12a. Answer: d) x⁶ f'(x) + 6x⁵ f(x)
<u>Step-by-step explanation:</u>
Use the multiplication formula for derivatives:
y = a · b → y' = a'b + ab'
<u>y = x⁶ · f(x) </u>
a = x⁶ b = f(x)
a' = 6x⁵ b' = f'(x)
<u>y' = a'b + ab'</u>
y' = 6x⁵ f(x) + x⁶ f'(x)
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12b. Answer: 
<u>Step-by-step explanation:</u>
Use the division formula for derivatives:
→ 

Note: You can also move the denominator to the top (it will have a negative exponent) and use the multiplication formula for derivatives.

<em>Translate into an algebraic equation:-</em>
<em>The quotient of a number and 5.</em>
<em />
<em />
✳︎ First, the word "quotient" indicates that we divide.
Here, we have the quotient of a number and 5, so we divide the number by 5; let the number be d.
So the quotient of d and 5 looks as follows:-

<h3>Good luck with your studies.</h3>

Answer:
18
Step-by-step explanation:
First you need to plug in the numbers for each variable.
3(3)+(5+2(8))-12
Now you solve
3(3)+(21)-12
9+21-12
18