Given that y = sin(x+y),find the derivative when (x, y)=(π,0)

Shown in the explanation

Recall that an implicit function is a relation given by the form:

Where is a function of two or more variables. In this case, that function is:

and is implicit because we can define it as:

having two variables.

So, let's take the derivative:

Applying chain rule:

But:

Therefore:

Isolating :

When :

{3 + i, 3 - i, 3, -1}

step-by-step explanation:

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870