Question

Antiderivative questions:
Let f(x) be function and
F(x) = f(x) - f^2 (x) + f^4 (x) -f^6 (x) +...+ (-1)^n * f^(2n) (x)+...

a) Find F'(x)
b) Find F''(x)
c) What is F'(x)sinx - F(x)cos(x)

Answer 1

I dont know if this is the same as just moving the exponent in front of the f and subtracting it by 1

Answer 2

\[F(x) = f(x) - f^2 (x) + f^4 (x) -f^6 (x) +...+ (-1)^n * f^{(2n)} (x)+...\]
Yeah that's the way

Answer 3

ok

Answer 4

thanks

Answer 5

You're welcome :)

Answer 6

im having difficulties with the last one. I dont know how this is supposed to simplifiy

Answer 7

nvm i got it