2007-03-09 18:14:51 · 4 answers · asked by All is Vanity 2 in Science & Mathematics ➔ Mathematics
it's: 3 sin^2 4x cos 4x * 4= 12 sin^2 4x cos 4x
it's solved by the chain rule: let y=4x, z=sin y, m=z^3,,, and find the derivatives of y,z,m, and multiply them!!!!
2007-03-09 18:21:28 · answer #1 · answered by A New Life 3 · 0⤊ 0⤋
d/dx f(g(x)) = f'(g(x))g'(x)
This function is made up of 3: 4x, sin (4x), sin^3 4x
Let t=4x, u=sin(t), then f(x)=u^3
f'(x) = 3u^2*u' = 3u^2 cos(t) * t' = 3u^2 * cos t * 4 =
= 12 sin^2 (4x) cos(4x)
2007-03-10 02:51:11 · answer #2 · answered by Amit Y 5 · 0⤊ 0⤋
f(x) = sin^3 4x
f'(x) = 12sin^2( 4x)cos^3(4x)
2007-03-10 02:21:32 · answer #3 · answered by Anonymous · 0⤊ 0⤋
f'(x) = 3sin^2(4x) * cos(4x) *4=12 sin^2(4x)*cos(4x)
2007-03-10 10:15:37 · answer #4 · answered by santmann2002 7 · 0⤊ 0⤋