Differentiate the explict funtion of 9x^2 + 64y^2 = 576
just use the chain rule to get
18x + 128y y' = 0
Now just solve for y'
and that's implicit, not explicit.
To differentiate the given equation, which is a function of two variables x and y, we need to use partial derivatives.
Let's start by differentiating the equation with respect to x:
Differentiating 9x^2 + 64y^2 = 576 with respect to x:
18x + 0 = 0
Simplifying, we get:
18x = 0
Now let's differentiate the equation with respect to y:
Differentiating 9x^2 + 64y^2 = 576 with respect to y:
0 + 128y = 0
Simplifying, we get:
128y = 0
From the partial derivatives, we can see that the derivative of the equation with respect to x is 18x = 0, and the derivative with respect to y is 128y = 0. However, since both of these equations simplify to 0 = 0, it implies that both the partial derivatives are always equal to zero.
Therefore, the explicit function of 9x^2 + 64y^2 = 576 is:
18x + 0 = 0 and 0 + 128y = 0
So, the explicit functions are:
18x = 0 and 128y = 0