Find the partial derivatives  for  the function f(x,y)=2x +3xy -5y^2?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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

`(del f)/(del x) = (del 2x)/(del x) + (del 3xy)/(del x) - (del 5y^2)/(del x)`

`(del f)/(del x) = 2 + 3y - 0`

`(del f)/(del x) = 2 + 3y`

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

`(del f)/(del y) = (del 2x)/(del y) + (del 3xy)/(del y) - (del 5y^2)/(del y)`

`(del f)/(del y) = 0 + 3x - 10y`

Hence, evaluating the partial derivatives, yields ` ` `(del f)/(del x) = 2 + 3y, (del f)/(del y) = 3x - 10y.`

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