2006-07-04 11:58:48 · 10 answers · asked by tq 3 in Science & Mathematics ➔ Mathematics
(15*14*13*12*11*10*9*8)x^7
2006-07-04 12:02:26 · answer #1 · answered by Ellie 1 · 5⤊ 1⤋
For a function of type y= x^n,
the r th derivative is = n(n-1)(n-2)...(n-r+1) x^(n-r) = nPr * x^(n-r), by successive differentiation.
Hence, the 8 th derivative of y=x^15 is
= 15*14*13*...*(15-8+1) *x^(15-8) = 15*14*13*...*8*x^7.
This may be rewritten as 15P8*x^7
2006-07-04 19:05:02 · answer #2 · answered by StreetX 2 · 0⤊ 0⤋
Considering that d/dx (x^n) = nx^(n-1) we get:
1: 15x^14
2: 210x^13
3: 2,730x^12
4: 32,760x^11
5: 360,360x^10
6: 3,603,600x^9
7: 3,2432,400x^8
8: 259,459,200x^7
2006-07-04 19:06:00 · answer #3 · answered by Jesse S 1 · 0⤊ 0⤋
First 15x^14
second (15)(14)x^13
third (15)(14)(13)x^12
and so on.......
answer ends up (15!-8!)x^7
2006-07-04 19:04:37 · answer #4 · answered by Anonymous · 0⤊ 0⤋
y(8) = 259459200x^7
2006-07-04 19:02:20 · answer #5 · answered by drakeflare73 2 · 0⤊ 0⤋
fifteen times fourteen times thirteen times twelve times eleven times ten times nine times eight times x to the seventh power
2006-07-04 19:05:28 · answer #6 · answered by cha_dooky_do 2 · 0⤊ 0⤋
y = x^15
y' = 15x^14
y'' = 210x^13
y''' = 2730x^12
y'''' = 32760x^11
y''''' = 360360x^10
y'''''' = 3603600x^9
y''''''' = 32432400x^8
y'''''''' = 259459200x^7
y = x^n
y' = nx^(n - 1)
The True formula for this is
y(mth derivative) = ((n!)/((n - m)!)) * x^(n - m)
n = 15
m = 8
y'''''''' = ((15!)/((15 - 8)!))) * x^(15 - 8)
y'''''''' = (15!/7!) * x^7
y'''''''' = 259459200x^7
2006-07-04 23:32:45 · answer #7 · answered by Sherman81 6 · 0⤊ 0⤋
d^8 y/dx^8 = (15!/7!) x^7
^_^
2006-07-05 07:27:54 · answer #8 · answered by kevin! 5 · 0⤊ 0⤋
come on! it's summer! no MATH!!!!!! nooooooooooooooo!
2006-07-04 19:57:05 · answer #9 · answered by Violet 3 · 0⤊ 0⤋
dy\dx=15x^14
y''=14*15*x^13
y'''=13*14*15*x^12
y(4)=12*13*14*15*x^11
y(5)=11*12*13*14*15*x^10
y(6)=10*11*12*13*14*15*x^9
y(7)=9*10*11*12*13*14*15*x^8
y(8)required=8*9*10*11*12*13*14*15*x^7=259459200*x^7
2006-07-04 19:05:05 · answer #10 · answered by zakizero 1 · 0⤊ 0⤋