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What is derivative f(x)=(-y-sin(x^3))?

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clara9391 | Student, Undergraduate | eNotes Newbie

Posted July 4, 2013 at 3:05 PM via web

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What is derivative f(x)=(-y-sin(x^3))?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 4, 2013 at 3:12 PM (Answer #1)

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You need to replace y for f(x), such that:

`y = -y - sin(x^3)`

You need to move the terms that contain y to the left side, such that:

`2y = -sin(x^3) => y = -(sin(x^3))/2`

You need to differentiate the function with respect to x, using the chain rule, such that:

`(dy)/(dx) = -(1/2)*(d(sin(x^3)))/(dx)*(d(x^3))/(dx)`

`(dy)/(dx) = -(1/2)*cos(x^3)*(3x^2)`

Hence, evaluating the derivative of the given function, using the chain rule, yields `(dy)/(dx) = -(3x^2*cos(x^3))/2` .

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