Find $\frac{d^{2} y}{d x^{2}}$ \[ y=\sqrt[5]{x} \]

Step 1 ：We are given the function \(y = x^{1/5}\).

Step 2 ：We are asked to find the second derivative of this function.

Step 3 ：First, we find the first derivative using the power rule for differentiation, which states that the derivative of \(x^n\) is \(n*x^{(n-1)}\).

Step 4 ：Applying the power rule, we get the first derivative as \(y' = 0.2x^{-0.8}\).

Step 5 ：Next, we find the second derivative by differentiating the first derivative.

Step 6 ：Applying the power rule again, we get the second derivative as \(y'' = -0.16x^{-1.8}\).

Step 7 ：Final Answer: The second derivative of the function \(y = x^{1/5}\) is \(\boxed{-\frac{0.16}{x^{1.8}}}\).