58th derivative of (1+x^3)^30 at x=0

[freshman2013]

Homework Statement

find the 58th derivative of (1+x^3)^(30) at zero (The Answer is zero)

Homework Equations

The binomial series expansion
the maclaurin series (f^(n)(0)/n!)x^n

The Attempt at a Solution

So I expanded the given equation into the binomial series and at at the 19th term, I got 30(30-1)...(30-19+1)/57! * x^(57). But I don't get how that gets me any closer to the answer of zero.

 

[Dick]

Homework Statement

find the 58th derivative of (1+x^3)^(30) at zero (The Answer is zero)

Homework Equations

The binomial series expansion
the maclaurin series (f^(n)(0)/n!)x^n

The Attempt at a Solution

So I expanded the given equation into the binomial series and at at the 19th term, I got 30(30-1)...(30-19+1)/57! * x^(57). But I don't get how that gets me any closer to the answer of zero.

First just figure out what powers of x could have a nonzero 58th derivative at zero. Try a few.