Find the derivative of w(r) = √{r^4 + 2}?

7 ⤊

2007-12-14 04:44:53 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

w'(r) = (1/2)(r^4 + 2)^(-1/2)4r^3
w'(r) = (2r^3)/[√(r^4 + 2)]

2007-12-14 05:34:18 · answer #1 · answered by Anonymous · 3⤊ 1⤋

if f(x)=âx
f'(x)=1/2âx
using this fact,
w(r)=sqrt(r^4+2)
dw/dr= 1/ sqrt(r^4+2) times (4r^3)
=4r^3 / 2 sqrt(r^4+2)

2007-12-14 12:58:53 · answer #2 · answered by cidyah 7 · 0⤊ 1⤋

dw/dr = (1/2) * (r^4 + 2)^(-1/2) * 4r^3 = (2r^3)/â{r^4 + 2}

2007-12-14 12:49:07 · answer #3 · answered by seminewton 3 · 1⤊ 1⤋

w(r) = (r^4 + 2)^(1/2)
w `(r) = (1/2) (r^4 + 2)^(-1/2) (4rÂ³)
w `(r) = (2rÂ³) / (r^4 + 2)^(1/2)

2007-12-14 19:27:30 · answer #4 · answered by Como 7 · 2⤊ 1⤋

(2r^3)/sqrt(r^4+2)

2007-12-14 12:49:22 · answer #5 · answered by Christophe G 4 · 1⤊ 0⤋