Need help with finding derivatives: the derivative of 1/3 x^3/2

[Jehelmer]

So, I already know that if you take the derivative of x^2 you get 2x, my problem is I can't seem to manage to figure out how to take the derivative of 1/3 x^3/2, any explanation would be much appreciated.

 

[Deleted member 4993]

So, I already know that if you take the derivative of x^2 you get 2x, my problem is I can't seem to manage to figure out how to take the derivative of 1/3 x^3/2, any explanation would be much appreciated.

Hint:

\(\displaystyle \dfrac{d}{dx}(c * x^n) \ = \ c * n * x^{(n-1)}\)

You know the correct answer for c = 1 and n = 2

Now calculate for c = 1/3 and n = 3/2.

If you are still stuck, come back showing your work.....

 

[stapel]

So, I already know that if you take the derivative of x^2 you get 2x, my problem is I can't seem to manage to figure out how to take the derivative of 1/3 x^3/2

Is the derivative any of the following?

. . . . .\(\displaystyle \mbox{a. }\, \dfrac{1}{\left(3\, \dfrac{x^3}{2}\right)}\)

. . . . .\(\displaystyle \mbox{b. }\, \dfrac{1}{3\, x^{{}^3/_2}}\)

. . . . .\(\displaystyle \mbox{c. }\, \dfrac{1}{3}\, \dfrac{x^3}{2}\)

. . . . .\(\displaystyle \mbox{d. }\, \dfrac{1}{3}\, x^{{}^3/_2}\)

Thank you!