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cabellos
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Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?
cabellos said:Iv forgotten the basics of this. How do we go about differentiating 3x^2 y^2 w.r.t y? I know the answer is 3x^2 y^2 but could someone explain this for me please?
cabellos said:ooops I am getting myself all confused now. I know how to do partial differentiation after all. I was reading the wrong solution as the question was z = x^2 y^2 and ofcourse dz/dy would = 3x^2 y^2 !
Partial differentiation is a mathematical concept used in calculus to determine the rate of change of a function with respect to one of its variables while holding all other variables constant. It is often used in multivariable calculus to analyze functions with multiple variables.
Ordinary differentiation involves finding the rate of change of a function with respect to one variable, whereas partial differentiation involves finding the rate of change with respect to one variable while holding all other variables constant. This allows for a more precise analysis of functions with multiple variables.
The notation used for partial differentiation is similar to ordinary differentiation, with the addition of subscripts to indicate which variable is being held constant. For example, the partial derivative of a function f with respect to x would be written as ∂f/∂x.
Partial differentiation has many practical applications, including in economics, physics, and engineering. It can be used to analyze the behavior of supply and demand curves, optimize production processes, and model physical systems with multiple variables.
There are several techniques used in partial differentiation, including the chain rule, product rule, and quotient rule. These rules are used to find the partial derivative of more complex functions by breaking them down into simpler parts and applying basic differentiation rules.