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Find `dy/dx` if `y=x^2 cos^3 2x`

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cflorie | Student, Undergraduate | (Level 1) eNoter

Posted July 2, 2012 at 6:09 PM via web

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Find `dy/dx` if `y=x^2 cos^3 2x`

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 2, 2012 at 6:19 PM (Answer #1)

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The function `y=x^2 cos^3 2x`

Using the product and the chain rules:

`dy/dx = (x^2)'*cos^3 2x + x^2(cos^3 2x)'`

=> `2x*cos^3 2x + x^2*2*3*cos^2 2x*(-sin 2x)`

=> `2x*cos^3 2x - 6*x^2*cos^2 2x*sin 2x`

The derivative `dy/dx` of `y=x^2 cos^3 2x` is `dy/dx = 2x*cos^3 2x - 6*x^2*cos^2 2x*sin 2x`

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