Question

Prove that, if:


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

Then:


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

By differentiating...

Answer 1

`y=(x^(n+1))/(n+1)+C\\\\ y'=\left((x^(n+1))/(n+1)+C\right)'\\ y'=\left((x^(n+1))/(n+1)\right)'+C'\\ y'=(1)/(n+1)\cdot (x^(n+1))'+0\\ y'=(1)/(n+1)\cdot (n+1)x^n\\ y'=x^n`