Question

Bright Minds, this is the last. Differentiate (x² + 1)(x - 1) using product rule​

Answer 1

Product rule:-

`\boxed{\sf (d)/(dx)uv=uv'+vu'}`

Let's solve

`\\ \sf\longmapsto (d)/(dx)(x^2+1)(x-1)`

`\\ \sf\longmapsto (x^2+1)(d)/(dx)(x-1)+(x-1)(d)/(dx)(x^2+1)`

`\\ \sf\longmapsto (x^2+1)+(x-1)(2x)`

`\\ \sf\longmapsto x^2+1+2x^2-2x`

`\\ \sf\longmapsto 3x^2-2x+1`

Answer 2

• Product rule:

`\sf (d)/(dx)uv=uv'+vu'`

`\longmapsto \sf ({x}^(2)+1)*\: (d)/(dx)(x - 1)+(d)/(dx)(x- 1) × (x^2 +1)`

`\longmapsto \sf ( {x}^(2)+1)+(x-1) (2x)`

`\longmapsto \sf x^2+1+2x^2-2x`

`\longmapsto \sf( {x}^(2) +1+ {2x}^(2) - 2x`

`\longmapsto \sf 3x^2-2x+1`