Find dy. \[ y=\cos \left(17 x^{2}\right) \]

Step 1 ：Given the function \(y=\cos \left(17 x^{2}\right)\), we are asked to find the derivative of \(y\) with respect to \(x\), denoted as \(dy\).

Step 2 ：We use 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 \(\cos(u)\) and its derivative is \(-\sin(u)\). The inner function is \(17x^{2}\) and its derivative is \(34x\).

Step 4 ：Applying the chain rule, we get \(dy = -\sin(17x^{2}) * 34x\).

Step 5 ：Simplifying, we get \(dy = -34x\sin\left(17x^{2}\right)\).

Step 6 ：So, the derivative of \(y=\cos \left(17 x^{2}\right)\) is \(\boxed{-34x\sin\left(17x^{2}\right)}\).