teng125 said:f(x,y)=arctan (y/x).
may i know what is the first partial derivative of this??
thanx
The formula for the first partial derivative of f(x,y)=arctan (y/x) is ∂f/∂x = -y/(x^2 + y^2).
To find the first partial derivative of f(x,y)=arctan (y/x), take the partial derivative with respect to x while treating y as a constant. This will result in ∂f/∂x = -y/(x^2 + y^2).
The first partial derivative of f(x,y)=arctan (y/x) represents the rate of change of the function with respect to x, while holding y constant. In other words, it shows how much the value of the function changes as x changes, with y remaining fixed.
Yes, the first partial derivative of f(x,y)=arctan (y/x) can be negative. This indicates that the function is decreasing as x increases, with y remaining constant.
The first partial derivative of f(x,y)=arctan (y/x) can be used to calculate the slope of a tangent line to the function at a specific point. This can be useful in fields such as physics, engineering, and economics, where rates of change and slopes are important in understanding and predicting real-world phenomena.