what is the fourth derivative of f(x)= (2x-3)^4?
2007-04-11 15:06:43 · 4 answers · asked by GHAAD 4 in Science & Mathematics ➔ Mathematics
Hi,
f(x)= (2x-3)^4
f'(x)= 4*(2x-3)^3*2 = 8*(2x - 3)^3
f"(x) = 24*(2x - 3)^2 * 2 = 48 * (2x - 3)^2
f'''(x) = 96*(2x - 3)*2 = 192(2x - 3)
f''''(x) = 192*2 = 384
You could also work out f(x) = (2x - 3)^4 =
(2x)^4 -4(2x)^3(3)+6(2x)^2(3)^2-4(2x)(3)^3+(3)^4 =
16x^4 - 96x^3 + 216x^2 - 216x + 81
f'(x) = 64x^3 - 288x^2 + 432x -216
f''(x) = 192x^2 -288x + 432
f'''(x) = 384x - 288
f''''(x) = 384
I hope this helps!! :-)
2007-04-11 15:22:11 · answer #1 · answered by Pi R Squared 7 · 0⤊ 0⤋
384. Just take the derivative 4 times.
2007-04-11 15:13:41 · answer #2 · answered by xjtoolx 1 · 0⤊ 0⤋
first= 4(2x-3)^3 *2
second= 24(2x-3)^2 *2
third= 96(2x-3)*2
Fourth= 384
2007-04-11 15:11:56 · answer #3 · answered by bruinfan 7 · 0⤊ 0⤋
f(x)' = 8(2x-3)^3
f(x)''= 48(2x-3)^2
f(x)'''= 192(2x-3)
f(x)''''= 384
2007-04-11 15:12:38 · answer #4 · answered by w1ckeds1ck312121 3 · 0⤊ 0⤋