To simplify differentiation, we rewrite <math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>x</mi><mo> + </mo><mn>1</mn></mrow></mfrac></math> as <math><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>-1</mn></mrow></msup></math>
Let's perform the differentiation: <math><mo>(</mo><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>-1</mn></mrow></msup><mo>)'</mo></math>
Apply the differentiation rule: <m><math><mo>(</mo><msup><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)'</mo><mo> = </mo><mi>n</mi><mo>·</mo><mo>(</mo><mi>f</mi><mo>)'</mo><mo>·</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>(</mo><mi>n</mi><mo> -</mo><mn>1</mn><mo>)</mo></mrow></msup></math></m> with <m>f</m> = <m><math><mi>x</mi><mo> + </mo><mn>1</mn></math></m>
 <math><mn>-1</mn><mo>·</mo><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)'</mo><mo>·</mo><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>-2</mn></mrow></msup></math>
 <math><mo>-</mo><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)'</mo><mo>·</mo><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>-2</mn></mrow></msup></math>
 <math><mo>-</mo><mfrac><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)'</mo></mrow><mrow><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math>
 <math><mo>-</mo><mfrac><mrow><mn>1</mn><mo> + </mo><mn>0</mn></mrow><mrow><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math>

▷<b>Answer: &nbsp; <math><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mo>(</mo><mi>x</mi><mo> + </mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math></b><span style='font-size:smaller'> &nbsp; &nbsp; (processing: 7 steps, 3 ms)</span>