I'm doing some homework right now and i have stumbled on a question that is asking to use order of operations, does multiplying and division go first or does adding and subtracting do? because my teacher has said adding and subtracting then division and multiplication? q: -7 x -3 + (-82)

You perform multiplication and division before addition and subtracting.

The order of operations can be remembered as PEMDAS: Parentheses, Exponentials, Multiplication, Division, Addition, Subtraction

Implicit differntiation, yeah
remember
the deritivive of f(x)/g(x)=(f'(x)g(x)-g'(x)f(x))/(g(x)^2)

so

2x+2y(dy/dx)=0
minus 2x
2y(dy/dx)=-2x
divide both sides by 2y
dy/dx=-x/y

take derivitve again
(-x'y-y'x)/(y^2)
remember, y'=dy/dx=-x/y
(-y-(-x/y)x)/(y^2)
at (4,3)
at x=4 and y=3
(-3-(-4/3)4)/(3^2)=
(-3+16/3)/9=
(-9/3+16/3)/9=
(7/3)/9=
7/27
the value is 7/27
it is concave up at that point btw