Posted by Sarah on Friday, June 15, 2012 at 12:16am.
a)
let z = cos x then dz/dx = -sin x
y = z^3
y' = 3 z^2 dz/dx
y' = 3 cos^2 x (-sin x)
= -3 sin x cos^2 x
b)
let z = x^3 then dz/dx = 3 x^2
y = sin z
y' = cos z dz/dx
= cos(x^3) (3 x^2)
= 3 x^2 cos x^3
c)y' = sin^2 x (-3sin 3x)+ cos 3x (2 sin x cos x
= -3sin 3x sin^2 x + 2 cos 3x sin x cos x
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