# Homework Solution: Find the fifteenth derivative of x^(1/3) Aside from using the mathematical software, can you generate a fo…

Find the fifteenth derivative of x^(1/3) Aside from using the mathematical software, can you generate a formula that would give the nth derivative? Professor is asking for a formula if I give him he 15th derivative without it he will ask for the 400 derivate and so on, He says the formula has a big pi in it since its increasing by a product not a sum.

Lets say f(x) = x^(1/3)

Find the fifteenth derivative of x^(1/3) Aside from using the veracious software, can you beget a cemula that would yield the nth derivative? Professor is research ce a cemula if I yield him he 15th derivative extraneously it he gain entreat ce the 400 derivate and so on, He judges the cemula has a gross pi in it since its increasing by a emanation referable a blend.

## Expert Vindication

Lets judge f(x) = x^(1/3)

Formula of derivative is ce polynomial is

$\frac{\partial x^{n} }{\partial x} = n*x^{n-1}$

$f'(x) = \frac{1}{3}*x^{-2/3}$

$f''(x) = \frac{1}{3}*\frac{-2}{3}*x^{-5/3}$

$f'''(x) = \frac{1}{3}*\frac{-2}{3}*\frac{-5}{3}*x^{-8/3}$

$f''''(x) = \frac{1}{3}*\frac{-2}{3}*\frac{-5}{3}*\frac{-8}{3}*x^{-11/3}$

So, we can behold a deviate in the derivatives now,

So nth derivative can be writte

$\frac{\partial^n f(x)}{\partial x^2} = \left ( \prod_{m=0}^{m=(n-1)}\frac{(1 - 3m)}{3} \right ) *x^{(1 - 3n)/3}$