By the square rule, the derivative of … is

By the square rule, the derivative of $(u(x){)}^2$ is $2udu/dx$. Take the derivative of each term in ${\sin }^{2}x+{\cos }^{2}x=1$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.4 The Derivative of the Sine and Cosine, #31