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derivative y=sin(e^(3x-x^2))? show how

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singup | Student, Grade 11 | eNoter

Posted January 3, 2012 at 10:56 PM via web

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derivative y=sin(e^(3x-x^2))?

show how

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 3, 2012 at 11:03 PM (Answer #1)

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You need to use chain rule to find derivative of function.

The chain rule tells that you need to differentiate with respect to x, from outside toward inside, such that:

`dy/dx = (sin(e^(3x-x^2)))'*(e^(3x-x^2))'*(3x-x^2)'`

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

Hence, the derivative of function is `dy/dx = (3- 2x)*(e^(3x-x^2))*(cos(e^(3x-x^2)))`

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