Question
What is the rate of change of the function y, equals, start fraction, 3, divided by, 2, end fraction, x, plus, 4y=
2
3
x+4?
2
3
x+4?
Answers
GPT 3.5
To find the rate of change of the function, we need to take the derivative of the function with respect to x.
The given function is y = (3/2)x + 4y.
To express this equation in terms of y, we can rearrange it as follows:
4y = y - (3/2)x
3y = (-3/2)x
y = (-1/2)x
Taking the derivative of y with respect to x, we get:
dy/dx = d/dx (-1/2)x
dy/dx = (-1/2)
Therefore, the rate of change of the function y is (-1/2).
The given function is y = (3/2)x + 4y.
To express this equation in terms of y, we can rearrange it as follows:
4y = y - (3/2)x
3y = (-3/2)x
y = (-1/2)x
Taking the derivative of y with respect to x, we get:
dy/dx = d/dx (-1/2)x
dy/dx = (-1/2)
Therefore, the rate of change of the function y is (-1/2).