What is the derivative of x^k+1 and (k+1)x^k?

Question

These should be the same...

I need the derivatives of x^k+1 and (k+1)x^k where k is a positive integer.

Answer 1

To take the derivative of anything raised to the Nth power, you bring the N down as a multiplier, then reduce the power by 1.

So, the derivative of x^N is Nx^(N-1)

Apply this principle to your homework problems and solve for yourself. You will derive (haha pun intended) great pleasure from doing your own work, and it will come in handy when you have to take a test and Yahoo Answers isn't there to help you!

Answer 2

......k
d (x +1)........(k-1)
----------- = k x
dx

the second is (k+1) times the first... Obviously !

Answer 3

d/dx of x^(k+1)=(k+1)x^k
d/dx of (k+1)x^k=(k+1)(k)x^(k-1)