Answered

IDNLearn.com: Where your questions meet expert advice and community insights. Ask anything and receive thorough, reliable answers from our community of 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 is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.