find the derivative of the function
(the square root of x sin x).
h(x)=√x sin x
2007-06-26 02:37:05 · 6 answers · asked by angel 1 in Science & Mathematics ➔ Mathematics
solve it as a product of two function
let f(x)=(x)^(1/2)
then f'(x)=1/√x
g(x)=sinx
g'(x)=cosx
product of f(x)g(x)=√xcosx + sinx/√x
2007-06-26 02:44:30 · answer #1 · answered by Anonymous · 0⤊ 0⤋
h `(x) = (1/2).x^(-1/2).sin x + cosx.√x
h `(x) = sin x / (2.√x ) + cos x.√x
2007-06-29 20:44:31 · answer #2 · answered by Como 7 · 0⤊ 0⤋
if h(x) = sqrt(xsinx)
h(x) = sqrt(x)*sqrt(sin x)
h(x) = (x)^1/2 * (sin x)^1/2
using product rule.
h(x) = 1/2((x)^-1/2)*(sin x)^1/2 + (1/2(cos x)^-1/2)x^1/2
2007-06-26 02:45:34 · answer #3 · answered by lilmaninbigpants 3 · 0⤊ 0⤋
chain rule and then product rule:
(1/2)(x sin(x))^(-1/2) * (sin(x) + x cos(x))
2007-06-26 02:47:53 · answer #4 · answered by PeteM 1 · 0⤊ 0⤋
h'(x)=(1/2)(x sin x)^(-1/2)*(sin(x)+xcosx)
2007-06-26 02:40:24 · answer #5 · answered by Not Eddie Money 3 · 0⤊ 1⤋
It really doesnt matter cause nobody will ever ask you that again.
2007-06-26 02:39:38 · answer #6 · answered by Jay S 1 · 0⤊ 2⤋