differentiate x*sin(x)
Let's perform the differentiation: <math><mo>(</mo><mi>x</mi><mo>·</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)'</mo></math> We differentiate <math><mi>U1</mi><mo>·</mo><mi>V2</mi></math> = <math><mi>x</mi><mo>·</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> using: <math><mo>(</mo><mi>U1</mi><mo>·</mo><mi>V2</mi><mo>)'</mo><mo> = </mo><mo>(</mo><mi>U1</mi><mo>)'</mo><mo>·</mo><mi>V2</mi><mo> + </mo><mi>U1</mi><mo>·</mo><mo>(</mo><mi>V2</mi><mo>)'</mo></math> Let's perform the differentiation <math><mi>U1</mi></math>: <math><mo>(</mo><mi>x</mi><mo>)'</mo></math> <math><mn>1</mn></math> Let's perform the differentiation <math><mi>V2</mi></math>: <math><mo>(</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)'</mo></math> <math><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> You can evaluate the resulted derivative (<math><mi>U1</mi><mo>·</mo><mi>V2</mi></math>)': <math><mn>1</mn><mo>·</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> + </mo><mi>x</mi><mo>·</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> <math><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> + </mo><mi>x</mi><mo>·</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> ▷<b>Answer: <math><mi>x</mi><mo>·</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> + </mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></b><span style='font-size:smaller'> (computation required 8 steps and 2 ms)</span>
