Question

Find d/dx((x^n+1)/(n+1))

I took photo of my textbook
ufile.io/vn0vh

Please go to the link . Is n here constant or variable?
Is there any need to use quotient rule??

Answer 1

n is a constant. Usually variables are letters in the last part of the alphabet.

So, if you mean

x^(n+1) / (n+1)

then using the power rule, the derivative is

(n+1)x^(n+1-1) / (n+1) = x^n

If you meant what you wrote, then the derivative is

(nx^(n-1)+0)/(n+1) = n/(n+1) x^(n-1)

for example,

d/dx x^(4+1)/5 = d/dx x^5/5 = x^4
d/dx (x^4+1)5 = 4/5 x^3