Answer
${dy}={-2{x}}\sin({{x}^2}){dx}$
Work Step by Step
We evaluate the function: $y=\cos({{x}^2})$
on differentiating the above:
$\frac{dy}{dx}=\frac{d\cos({{x}^2})}{dx}$
or $\frac{dy}{dx}=-\sin({{x}^2})\frac{d({x})^2}{dx}$
or $\frac{dy}{dx}={-2{x}}\sin({{x}^2})$
or ${dy}={-2{x}}\sin({{x}^2}){dx}$
The final answer is: ${dy}={-2{x}}\sin({{x}^2}){dx}$
