Find the derivative of the function $y=5 x e^{x^{6}}$

Step 1 ：The question is asking for the derivative of the function \(y=5 x e^{x^{6}}\). To solve this, we can use the product rule and the chain rule of differentiation. The product rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 2 ：Applying the product rule and the chain rule, we get the derivative as \(30x^{6}e^{x^{6}} + 5e^{x^{6}}\).

Step 3 ：Final Answer: The derivative of the function \(y=5 x e^{x^{6}}\) is \(\boxed{30x^{6}e^{x^{6}} + 5e^{x^{6}}}\).