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Differentiate with respect to x.

cos x3

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Chain rule:

If y = f(t) and t = g(x) then dy/dx = dy/dt x dt/dx

Let y = cos x3

If t = x3 then cos x3= cos t or y = cos t

dy/dt = -sin t

dt/dx = 3x2

Now,

dy/dx = dy/dt x dt/dx = 3 x2 (-sin t)

Substituting the value of t back, we get

dy/dx = 3 x2 (-sin x3)

= -3 x2 sin x3

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