In an electric field, the lines of force are perpendicular to the curves of equal electric potential, In a certain electric field, a curve of equal potential is $y=\sqrt{2 x^{2}+8}$. If the line along which the force acts on an electron has an inclination of $135^{\circ}$, find its equation.

Find $\frac{d y}{d x}$.
\[
\frac{d y}{d x}=
\]

Step 1 ：Rewrite the equation as \(y=(2x^2+8)^{1/2}\)

Step 2 ：Apply the chain rule for differentiation, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function

Step 3 ：The outer function is \(u^{1/2}\) and its derivative is \(\frac{1}{2}u^{-1/2}\)

Step 4 ：The inner function is \(2x^2+8\) and its derivative is \(4x\)

Step 5 ：So, \(\frac{dy}{dx} = \frac{1}{2}(2x^2+8)^{-1/2} \cdot 4x\)

Step 6 ：Simplify this to get \(\frac{dy}{dx} = \frac{2x}{\sqrt{2x^2+8}}\)

Step 7 ：So, the derivative of \(y\) with respect to \(x\) is \(\boxed{\frac{2x}{\sqrt{2x^2+8}}}\)