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Calculate the partial derivative indicated: `f(x,y)=2xy+y^2`; `(df)/(dx) (x, y),...

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Calculate the partial derivative indicated: `f(x,y)=2xy+y^2`; `(df)/(dx) (x, y), (df)/(dy) (x, y)`

 

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You need to evaluate the partial derivative ` (del f)/(del x),` hence, you need to differentiate the given function with respect to x, considering y as constant, such that:

`(del f)/(del x) = (del 2xy)/(del x) + (del y^2)/(del x)`

`(del f)/(del x) = 2y + 0 => (del f)/(del x) = 2y`

You need to evaluate the partial derivative `(del f)/(del y),` hence, you need to differentiate the given function with respect to y, considering x as constant, such that:

`(del f)/(del y) = (del 2xy)/(del y) + (del y^2)/(del y)`

`(del f)/(del y) = 2x + 2y`

Hence, evaluating the partial derivatives `(del f)/(del x), (del f)/(del y)` , yields `(del f)/(del x) = 2y, (del f)/(del y) = 2x + 2y.`

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