- #1
hthorne21
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Find fyy (x,y) where f(x,y) = x2y3 + x4y + xe2y
A partial derivative is a mathematical concept used to determine the rate of change of a function with respect to one of its variables, while holding all other variables constant.
Partial derivatives are used to determine the rate of change of a function with respect to one variable, while keeping all other variables constant. Regular derivatives, on the other hand, determine the rate of change of a function with respect to a single variable.
To find partial derivatives, you must first identify the variable that you are differentiating with respect to. Then, treat all other variables as constants and use the power rule to differentiate the function. Repeat this process for each variable in the function.
The partial derivative of x^{2}y^{3} + x^{4}y + xe^{2y} with respect to x is 2xy^{3} + 4x^{3}y + e^{2y}.
The partial derivative of x^{2}y^{3} + x^{4}y + xe^{2y} with respect to y is 3x^{2}y^{2} + x^{4} + 2xe^{2y}.