Let

{eq}z = \frac{xy}{4y^2 - 5x^2} . {/eq} Then find

{eq}\frac{\partial z}{\partial x},\text{ and } \frac{\partial z}{ \partial y} . {/eq}

Question:

Differentiable Functions; Partial Derivatives:

We want to find the partial derivatives

{eq}z_x= \frac{\partial z}{\partial x}, \text{ and }z_y=\frac{\partial z}{\partial y} , {/eq}

of the differentiable function {eq}z =z(x,y)= \frac{xy}{4y^2 - 5x^2}. {/eq}

We'll recall that for each partial derivative, say with respect to one of the variables, we can apply the usual rules of differentiation, as long as we take as a constant the other variables appearing in the expression.

Answer and Explanation: 1