Find the value of partial z / partial x at the point (1, 1, 1) if the equation 8 x y + z^3 x - 4...

Question:

Partial Differentiation:

Partial differentiation of a function of two or more variables with respect to a particular variable is obtained by differentiating the fuction with only one variable and keeping the remaining variables constant at the same time. It represents the rate of change of the function with respect to only variables. Some formulas of differentiation that are generally utilized to differentiate a function are listed below:

$$\begin{align} \\ &\hspace{1cm} \dfrac{\text{d}c}{\text{d}x} =0 & & \left[\text{ Where } c\ \text{is constant value } \right]\\[0.3cm] &\hspace{1cm} \dfrac{\text{d}}{\text{d}x} x^n =nx^{n-1} & & \left[\text{ This is power rule of differentiation } \right]\\[0.3cm] &\hspace{1cm}\displaystyle \dfrac{\text{d}}{\text{d}x} \left[ uv \right]=u \frac{\text{d}v}{dx}+v\frac{\text{d}u}{dx} && \left[\text{ This is product rule of differentiation } \right]\\[0.3cm] &\hspace{1cm} \frac{\text{d}}{\text{d}x}f(g(x)) =f'(g(x)) g'(x) && \left[\text{ This is chain rule of differentiation } \right]\\[0.3cm] \end{align}\\ $$

Answer and Explanation: 1