Partial Derivatives

For a function of two independent variables, f(x,y), the partial derivative of f
with respect to x denoted by f_x , we can be found f_x by applying all the usual rules of differentiation. The only exception is that, whenever and wherever the second variable y appears, it is treated as a constant in every respect. The partial derivative of f with respect to y denoted by f_y , we can similarly be found by treating x as a constant whenever it appears.
For a function of more than two independent variables, the same method applies. Its partial derivative with respect to x, can be obtained by differentiating it with respect to x, using all the usual rules of differentiation. Except that all the other independent variables, whenever and wherever they occur in the expression of f, are
treated as constants.
f_x or ?f/?x means partial derivative of f with respect to x
f_y or ?f/?y means partial derivative of f with respect to y

For a function of two independent variables, f(x,y), the partial derivative of f
with respect to x denoted by f_x , we can be found f_x by applying all the usual rules of differentiation. The only exception is that, whenever and wherever the second variable y appears, it is treated as a constant in every respect. The partial derivative of f with respect to y denoted by f_y , we can similarly be found by treating x as a constant whenever it appears.
For a function of more than two independent variables, the same method applies. Its partial derivative with respect to x, can be obtained by differentiating it with respect to x, using all the usual rules of differentiation. Except that all the other independent variables, whenever and wherever they occur in the expression of f, are
treated as constants.
f_x or ?f/?x means partial derivative of f with respect to x
f_y or ?f/?y means partial derivative of f with respect to y