Partial Derivative with Respect to y of a*cos(xy)-y*sin(xy)

In summary, a partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables while holding all other variables constant. It differs from a regular derivative in that it calculates the rate of change of a multivariable function with respect to one variable. Finding a partial derivative is important in various fields of science, and the notation used for partial derivatives is similar to regular derivatives but with a slight difference. Some common applications of partial derivatives include optimization, economics, and physics.
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Homework Statement


Find the partial derivative of a*cos(xy)-y*sin(xy) with respect to y.

Homework Equations


None.

The Attempt at a Solution


The answer is -ax*sin(xy)-sin(xy)-xy*cos(xy).
I know that I need to treat x as constant since I need to take the partial derivative with respect to y. But I don't know how to get -sin(xy). I know how to get -ax*sin(xy) and -xy*cos(xy).
 
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Never mind. I got it.
 
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How do I delete this thread?
 

Related to Partial Derivative with Respect to y of a*cos(xy)-y*sin(xy)

1. What is a partial derivative?

A partial derivative is a mathematical concept that measures the rate of change of a function with respect to one of its variables, while holding all other variables constant.

2. How is a partial derivative different from a regular derivative?

A regular derivative calculates the rate of change of a function with respect to one variable, while a partial derivative calculates the rate of change of a multivariable function with respect to one variable, while holding all other variables constant.

3. Why is finding a partial derivative important?

Finding a partial derivative is important in many fields of science, such as physics, engineering, and economics. It allows us to understand how a function changes with respect to a specific variable, which can help us make predictions and solve problems in real-world scenarios.

4. What is the notation used for partial derivatives?

The notation used for partial derivatives is similar to regular derivatives, but with a slight difference. Instead of using the prime symbol (') to indicate differentiation, we use the symbol ∂ (pronounced "partial"). For example, the partial derivative of a function f(x, y) with respect to x would be written as ∂f/∂x.

5. What are some common applications of partial derivatives?

Partial derivatives have many applications in fields such as optimization, economics, and physics. For example, in optimization problems, we use partial derivatives to find the minimum or maximum value of a function. In economics, partial derivatives are used to calculate marginal costs and marginal revenue. In physics, they are used to calculate rates of change in complex systems, such as in thermodynamics or fluid mechanics.

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