I got
(4x + 15)/[3(4x + 5)^5/3]
2006-10-14 06:39:45 · 6 answers · asked by chris 2 in Science & Mathematics ➔ Mathematics
Quotient rule:
[(4x+5)^(1/2) - x(1/2)(4x+5)^(-1/2)4] / (4x+5).
Multiply top and bottom by (4x+5)^(1/2):
[4x+5 - 2x] / (4x+5)^(3/2), or
(2x+5) / (4x+5)^(3/2).
2006-10-14 06:51:41 · answer #1 · answered by James L 5 · 0⤊ 0⤋
Quotient Rule if f(x)=u/v then f'(x)=(vu'-uv')/v^2
so f'(x)= ((4x+5)^1/2-2x(4x+5)^-1/2)/(4x+5)
rearrange the solution you should get
f'(x) = (2x+5)/(4x+5)^3/2
2006-10-14 07:06:15 · answer #2 · answered by Anonymous · 0⤊ 0⤋
f(x)= x*1/(4x+5)^1/2
f '(x)=1/(4x+5)^1/2+(x)(4/2(4x+5))=(2x+5)/(4x+5)^3/2
2006-10-14 09:49:19 · answer #3 · answered by Sam 2 · 0⤊ 0⤋
I got 8 * sqroot(4x + 5)
2006-10-14 06:51:03 · answer #4 · answered by Jerm 1 · 0⤊ 0⤋
f'(x)=[(4x+5)^(1/2) - (x)(1/2)(4x+5)^(-3/2)(4)]/(4x+5)
2006-10-14 06:46:37 · answer #5 · answered by Greg G 5 · 0⤊ 0⤋
f[x]=x/sqrt(4x+5)
f[x]^2=x^2/4x+5
f[x]^2*[4x+5]=x^2
differentiating we have
2f[x]*f'[x][4x+5]+f[x]^2*4=2x
f'[x][2f(x)][4x+5]=2x-4x^2/4x+5
f'[x]=2x[1-2x]/[4x+5]/[2x/sqrt[4x+5]*1/[4x+5]
=[1-2x]/[4x+5]^3/2
2006-10-14 07:07:00 · answer #6 · answered by openpsychy 6 · 0⤊ 0⤋