Partial derivatives (35 pts):

could someone explain me why this partial derivative gives me this solution. i already have the answer but i don't really get how it works without working out the brackets.



could someone explain me the rule?

A partial derivative of a function of several variables is a derivative of one of those variables.

The answer is in the notation du/dy. It states the change in U based on the change in Y. so it is not asking for the change in X therefor we can view 4(x+5) as a constant instead of a variable. It might look better if you looked at it like this f(u)=4(x+5)(y+5)^2 so du/dy we just want the derivative of Y so ignore the rest and just do the derivative where Y is involved (y+5)^2 which is 2(y+5) then add in the rest of the equation because it is considered a constant. An example of this is like f(u)=10(y+5)^2, f'(u)=du/dy=(10)(2)(y+5). Hope that helps explain it better.

Step-by-step explanation:

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are