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Given y=sin(cosx) what is dy/dx?

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olaf | Student, Grade 11 | eNoter

Posted May 23, 2011 at 1:20 AM via web

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Given y=sin(cosx) what is dy/dx?

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giorgiana1976 | College Teacher | Valedictorian

Posted May 23, 2011 at 1:23 AM (Answer #1)

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We'll have to differentiate the given function y with respect to x.

y = sin (cos x)

We'll differentiate both sides:

dy = [sin (cos x)]'dx

We'll differentiate using chain rule, since the given function is the result of composition of two functions:

dy/dx = [cos (cos x)]*(cos x)'

dy/dx = (-sin x)*[cos (cos x)]

The requested  expression for dy/dx is: dy/dx = (-sin x)*[cos (cos x)].

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