Question

Find the derivative of the summation from n equals 0 to infinity of the quotient of the product of negative 1 raised to the nth power and x raised to the quantity 2 times n plus 1 power and the product of 3 to the 2 times n power and the square of n factorial . Write your answer as a summation with lower limit of summation equal to 0. (10 points) Please explain with steps

Answer 1

gee, ever think of using actual math? Starting with
∞
∑ (-1)^n / (3^(2n) * (n!)^2) x^(2n+1)
n=0

just use the power rule on each term.
∞
∑ (-1)^n * (2n+1) / (3^(2n) * (n!)^2) x^(2n)
n=0

This is just a Bessel Function

Answer 2

Gee, think of not being toxic