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

User Damir
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2 Answers

11 votes

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

User Privatehuff
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8 votes

Answer:

  • 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

User Vizcayno
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