Answered

Find answers to your questions faster and easier with IDNLearn.com. Join our community to receive prompt and reliable responses to your questions from experienced professionals.

Prove that, if:

[tex]y=\frac { { x }^{ n+1 } }{ n+1 } +C[/tex]

Then:

[tex]\\ \\ \frac { dy }{ dx } ={ x }^{ n }[/tex]

By differentiating...

Sagot :

Konrad509idn
[tex]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 [/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.