Partial Derivative fy(x,y): What Is It?

Thread starter squenshl
Start date Aug 2, 2009
Tags

Derivative Partial Partial derivative

In summary, a partial derivative of fy(x,y) is a mathematical concept used in calculus to measure the rate of change of a function with respect to one of its variables, while holding all other variables constant. It is calculated by taking the derivative of the function with respect to the designated variable, treating all other variables as constants. The significance of a partial derivative of fy(x,y) lies in its usefulness in understanding how a function changes in relation to one of its variables, and it is commonly used in multivariable calculus to solve real-world problems. A partial derivative of fy(x,y) can be negative, indicating a decrease in the function, and there are limitations to its use, such as assuming continuity and differentiability of the function and

Aug 2, 2009

squenshl

Given that f(x,y) = x|y|
I know that f_x(x,y) = |y| but what is f_y(x,y).
Thanks heaps.

Physics news on Phys.org

Aug 2, 2009

Homework Helper

Gold Member

Hint: Break it up into two cases: If y > 0, then f(x,y) = xy. If y < 0, then f(x,y) = -xy.

Aug 2, 2009

HallsofIvy

Science Advisor

Homework Helper

Note that g(y)= |y| is not differentiable at y= 0 so f(x,y)= x|y| has no partial derivative, with respect to y, on the line y= 0.

Related to Partial Derivative fy(x,y): What Is It?

What is a partial derivative of fy(x,y)?

A partial derivative of fy(x,y) is a mathematical concept used in calculus to measure the rate of change of a function with respect to one of its variables, while holding all other variables constant. It is denoted as ∂fy(x,y) or fy(x,y).

How is a partial derivative of fy(x,y) calculated?

A partial derivative of fy(x,y) is calculated by taking the derivative of the function with respect to the designated variable, treating all other variables as constants. This can be done using the basic rules of differentiation, such as the power rule, product rule, and chain rule.

What is the significance of a partial derivative of fy(x,y)?

The partial derivative of fy(x,y) is useful in understanding how a function changes in relation to one of its variables. It is commonly used in multivariable calculus to optimize functions and solve real-world problems in fields such as physics, economics, and engineering.

Can a partial derivative of fy(x,y) be negative?

Yes, a partial derivative of fy(x,y) can be negative. This indicates that the function is decreasing with respect to the designated variable. A positive partial derivative indicates that the function is increasing, while a zero partial derivative indicates that the function is constant.

Are there any limitations to using partial derivatives of fy(x,y)?

One limitation of using partial derivatives of fy(x,y) is that it assumes that the function is continuous and differentiable. Additionally, it only measures the rate of change in one direction and does not account for changes in other directions. In some cases, other methods such as directional derivatives may be necessary to fully understand the behavior of a multivariable function.