Let f(x) = e^(x^(3)). Calculate the 9th derivative
f^(9)(0) using the exponential series and Taylor’s formula.

Question

Let f(x) = e^(x^(3)). Calculate the 9th derivative 
f^(9)(0) using the exponential series and Taylor’s formula.

kainui · Answer

What part are you needing help with? You surely know how to find every derivative up to the 9th, right? If not, we can talk about that or talk about what taylor's formula is if that's where you're having difficulty. Taylor and Mclauren series just mean that you're making a polynomial function that has the same derivatives at a point, up to as many derivatives as you take.

australopithecus · Answer

yes I know how to find there derivative up to the 9th. I just don't know how to answer this

anonymous · Answer

9!/3!

anonymous · Answer

$$ \large e^{x^3}= \sum_{n=0}^\infty \frac{x^{3n}}{n!}$$
Now I would expand it