Find {eq}\dfrac{ \partial z}{\partial x} {/eq} and {eq}\dfrac{ \partial z}{\partial y}. {/eq}

{eq}z = x^8 \ln (1 + xy^{ - \frac{5}{7}}) {/eq}

Question:

Partial Differentiation:

Partial differentiation is the process to find the derivative of a function which includes more than one variables. Here, as the function consists of two variables x and y. So, to find the partial derivative with respect to one variable, keep the other variable as constant.

Also,

{eq}\dfrac{d}{dx} (x^n) = nx^{n -1} \\ \dfrac{d}{dx} (\ln x) = \dfrac{1}{x} {/eq}

Answer and Explanation: 1