You're correct, the answer is C.
Given any function of the form 

, then the derivative of y with respect to x (

) is written as:

In which 

 is any constant, this is called the power rule for differentiation.
For this example we have 

, first lets get rid of the quotient and write the expression in the form 

:

Now we can directly apply the rule stated at the beginning (in which 

):

Note that whenever we differentiate a function, we simply "ignore" the constants (we take them out of the derivative).
 
        
             
        
        
        
Answer:
y"(2, 1) = -5
Step-by-step explanation:
Step 1: Define implicit differentiation
5 - y² = x²
Step 2: Find dy/dx
- Take implicit differentiation: -2yy' = 2x
 - Isolate y': y' = 2x/-2y
 - Isolate y': y' = -x/y
 
Step 3: Find d²y/dx²
- Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
 - Substitute y': y" = [-y - (-x/y)(-x)] / y²
 - Simplify: y" = [-y - x²/y] / y²
 - Multiply top/bottom by y: y" = (-y² - x²) / y³
 - Factor negative: y" = -(y² + x²) / y³
 
Step 4: Substitute and Evaluate
y"(2, 1) = -(1² + 2²) / 1³
y"(2, 1) = -(1 + 4) / 1
y"(2, 1) = -5/1
y"(2, 1) = -5
 
        
             
        
        
        
Answer:
90.5
Step-by-step explanation:
Velocity is a time-derivative of displacement or the height, in this case.


At maximum height, the velocity is 0 and the height is 128.
Substitute these values into both equations above,


From the first equation,

Substitute for 
.





 
        
             
        
        
        
Answer:
V≈157.08
Step-by-step explanation:
I hope this helps 
 
        
             
        
        
        
I feel like the answer is 16. 2 pound container with 1/8 trail mix