Compute the first-order partial derivatives. z=xy

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Compute the first-order partial derivatives.  z=xy

Toni Scott · Accepted Answer

Step 1&amp;nbsp;When calculating partial derivatives for a function with several variables, one variable is assumed to be constant while the other variable is differentiated. For instance, using y as a constant and differentiating with regard to the other variable, a function with two variables, x, and y, can have its partial derivative with respect to x determined.By treating x as a constant and differentiating with respect to y, one can calculate the partial derivative with respect to y. The function for the described situation consists of two variables. So either partial derivative with respect to x or partial derivative with respect to x will be the first-order partial derivatives.Step 2&amp;nbsp;Given function is&amp;nbsp;z=xy. First calculate the partial derivative with respect to x. Here, treat y as a constant.&amp;nbsp;zx=∂∂x(xy)&amp;nbsp;=1y∂∂x(x)&amp;nbsp;=1y⋅1&amp;nbsp;=1y&amp;nbsp;Do a partial derivative calculation with respect to y now. Here, consider x to be a constant.zy=∂∂y(xy)&amp;nbsp;=x∂∂y(1y)&amp;nbsp;=x⋅∂∂y(y−1)&amp;nbsp;=x⋅(−y−2)&amp;nbsp;=−xy2

servidopolisxv · Accepted Answer

The required is to compute the first-order partial derivatives:z=xyThe first-order partial derivatives:∴zx=∂∂x(xy)=1y∴zy=∂∂y(xy)=∂∂y(xy−1)=−xy−2=−xy2Result:zx=1y′zy=−xy2

Compute the first-order partial derivatives. z=x/y

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