Let's differentiate: <math><mo>(</mo><mi>cos</mi><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo><mo>)'</mo></math>
Apply the differentiation rule: <m><math><mo>(</mo><mi>cos</mi><mo>(</mo><mi>f</mi><mo>)</mo><mo>)'</mo><mo> = </mo><mo>-</mo><mo>(</mo><mi>f</mi><mo>)'</mo><mo>·</mo><mi>sin</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></m> with <m>f</m> = <m><math><mn>2</mn><mi>x</mi></math></m>
 <math><mo>-</mo><mo>(</mo><mn>2</mn><mi>x</mi><mo>)'</mo><mo>·</mo><mi>sin</mi><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></math>

▷<b>Result: &nbsp; <math><mo>-</mo><mn>2</mn><mo>·</mo><mi>sin</mi><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></math></b><span style='font-size:smaller'> &nbsp; &nbsp; (computation required 3 steps and 1 ms)</span>