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What is the slope of the tangent to the curve: y= 6sin2x at x=60 degrees?

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foxwit | Student, Undergraduate | (Level 1) Salutatorian

Posted August 23, 2012 at 8:15 PM via web

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What is the slope of the tangent to the curve:

y= 6sin2x

at x=60 degrees?

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lfryerda | High School Teacher | (Level 2) Educator

Posted August 23, 2012 at 8:34 PM (Answer #1)

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The slope of the tangent to a function is found by taking the derivative of the function, then evaluating at the appropriate value of x.

This means the derivative of `y=6sin2x` is 

`y'=12cos2x`    using the chain rule

and the slope is found at `x=60^circ=pi/3` which gives

`y'(pi/3)=12cos({2pi}/3)`    use the CAST rule

`=12(-1/2)`

`=-6`

The slope of the tangent is -6

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