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I have z=(e^y)φ*[y*e^(x^2/2y^2)].I have to prove that y*(dz/dx) -x*(dz/dy)=0.First of all what does φ mean there?
Are you sure that this isn't specified in the problem or earlier in the text? My first guess is that it's just some number and that it won't contribute to the final result. But the only way I can verify that is to assume that it is, and then solve the problem under that assumption. This seems like something you should try yourself. Have you tried to compute the partial derivatives of the z defined byElaia06 said:I have z=(e^y)\varphi*[y*e^(x^2/2y^2)].I have to prove that y*(dz/dx) -x*(dz/dy)=0.First of all what does φ mean there?
Elaia06 said:I have z=(e^y)φ*[y*e^(x^2/2y^2)].I have to prove that y*(dz/dx) -x*(dz/dy)=0.First of all what does φ mean there?
A partial derivative is a mathematical concept that is used to measure the rate of change of a multivariable function with respect to one of its variables while holding all other variables constant. It is denoted by ∂ (pronounced "partial") and is commonly used in fields such as physics, engineering, and economics.
To calculate a partial derivative, you take the derivative of a function with respect to one variable while treating all other variables as constants. This means that you will have multiple partial derivatives for a single multivariable function, each one representing the rate of change in a different variable.
Partial derivatives are important because they allow us to analyze how changes in one variable affect the overall behavior of a multivariable function. They are also used to optimize functions in fields such as economics, where finding the maximum or minimum value of a function is crucial.
Partial derivatives are used in various real-life applications, including economics, physics, engineering, and statistics. For example, in economics, partial derivatives are used to analyze how changes in one variable, such as price, affect the demand or supply of a product. In physics, partial derivatives are used to calculate the rate of change of a physical quantity with respect to time or other variables.
The main difference between a partial derivative and a total derivative is the number of variables involved. A partial derivative is calculated with respect to one variable while holding all other variables constant, while a total derivative is calculated with respect to all variables in a multivariable function. Additionally, a total derivative takes into account the effect of changes in all variables on the overall behavior of the function, while a partial derivative only considers the effect of changes in one variable.