Differentiate sin(x)cos(x) using the product rule.

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))' = cos²(x) - sin²(x)