2007-03-10 03:26:27 · 4 answers · asked by Math girl 1 in Science & Mathematics ➔ Mathematics
F(x)=(x-1)(x+1)(x^2+1)(x^4+1) .. (x^1024 + 1)
= (x^2-1)(x^2+1)(x^4+1) ... (x^1024 + 1)
= (x^4 - 1)(x^4 + 1) (x^8+1) ... (x^1024 + 1)
= ....
= (x^1024 - 1)(x^1024 + 1)
= (x^2048 - 1)
df/dx = 2048 x^2047
2007-03-10 04:20:57 · answer #1 · answered by Mena M 3 · 1⤊ 0⤋
F(x)=(x-1)(x+1)(x^2+1)(x^4+1)
= (x^2-1)(x^2+1)(x^4+1)
=(x^4-1)(x^4+1)
=x^8-1
So F'(x) = 8x^7
2007-03-10 12:00:51 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
The function F simplifies to:
F(x) = x^2048 - 1
So the derivative is: F'(x) = 2048*x^2047
2007-03-10 11:34:54 · answer #3 · answered by Anonymous · 1⤊ 1⤋
There are two ways. (a) Use the chain rule. (b) Do the multiplication, and then differentiate term by term. I much prefer the second method.
2007-03-10 11:30:25 · answer #4 · answered by Anonymous · 0⤊ 0⤋