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Anonymous Anonymous
  • 20-02-2015
  • Mathematics
Answered

Prove that, if:


\(y=\frac { { x }^{ n+1 } }{ n+1 } +C\)


Then:


\(\\ \\ \frac { dy }{ dx } ={ x }^{ n }\)


By differentiating...

Verified Answer :

konrad509
konrad509 konrad509
  • 20-02-2015

\(y=\dfrac{x^{n+1}}{n+1}+C\\\\ y'=\left(\dfrac{x^{n+1}}{n+1}+C\right)'\\ y'=\left(\dfrac{x^{n+1}}{n+1}\right)'+C'\\ y'=\dfrac{1}{n+1}\cdot (x^{n+1})'+0\\ y'=\dfrac{1}{n+1}\cdot (n+1)x^n\\ y'=x^n\)

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