find the derivative
2006-12-04 08:59:59 · 5 answers · asked by pago 1 in Science & Mathematics ➔ Mathematics
First, evaluate the derivative of the two inner sine functions using the chain rule. Then, evaluate the derivative with the third sine function added, using the chain rule again.
d/dx sin(sin(x)) = cos(sin(x))*cos(x)
d/dx sin(sin(sin(x))) = cos(sin(sin(x))) *
cos(sin(x))*cos(x)
2006-12-04 09:03:33 · answer #1 · answered by عبد الله (ドラゴン) 5 · 1⤊ 1⤋
Remember that the chain rule works as follows.
if y = sin(box), then
y' = cos(box)[box prime] or
y' = cos(box)[derivative of box]
This example is no different.
y = sin (sin (sinx)))
y' = cos (sin (sinx)) * cos(sinx) * cosx
2006-12-04 09:03:52 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
f(x)=h(g(x))
f'(x)=h'(g(x))*g'(x)
y=f(x) y'=f'(x)=cos(sin(sin(x))*cos(sin(x))*cos(x)
http://en.wikipedia.org/wiki/Derivative
2006-12-04 09:12:55 · answer #3 · answered by crys 2 · 0⤊ 0⤋
y'= cos(sin(sinx))cos(sinx)cosx
2006-12-04 09:02:42 · answer #4 · answered by Milo 4 · 0⤊ 0⤋
y' = cos(sin(sin(x))) (sin (sin(x))'
y' = cos(sin(sin(x))) cos (sin(x)) (sin (x))'
y' = cos(sin(sin(x))) cos(sin(x)) cos(x)
2006-12-04 09:07:57 · answer #5 · answered by MsMath 7 · 1⤊ 1⤋