Is the derivative of (sin(X))^3 = 3(cos(X))?

1 ⤊

Is the derivative of (sin(X))^3 = 3(cos(X))?

2007-09-06 07:59:44 · 4 answers · asked by Mike B 2 in Science & Mathematics ➔ Mathematics

4 answers

f (x) = ( sin x ) ³
f `(x) = 3 (sin ² x) (cos x)

2007-09-06 08:21:34 · answer #1 · answered by Como 7 · 1⤊ 0⤋

No
(sin(x))^3=[3(sin(x))^2]*cos x

2007-09-06 15:06:01 · answer #2 · answered by dkmu 1 · 0⤊ 0⤋

no

y = (sin(X))^3
=> dy/dx = 3 sin^2 x * cos x

2007-09-06 15:04:40 · answer #3 · answered by harry m 6 · 0⤊ 0⤋

(sin(x))^3
substitute sin(x) = y
differentiating with respect to x
cos(x)dx = dy
so dy/dx = cosx
now [sin(x)]^3 = y^3
differentiating y^3 with respect to x
3y^2 dy/dx
substituting back y =sinx and dy/dx = cosx
3(sin(x))^2 cos(x)
so differential of [sin(x)]^3 = 3[sin(x)]^2 cos(x)

2007-09-06 15:15:19 · answer #4 · answered by mohanrao d 7 · 0⤊ 0⤋