Find the derivative of the following function: `y = cot (sqrt(2x))`

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lemjay | High School Teacher | (Level 3) Senior Educator

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`y = cot (sqrt(2x))`

Before taking the derivative, express the radical as an exponent.

`y = cot((2x)^(1/2))`

Then, apply the derivative formula:

`(cot u)' = -csc^2 u * u'`

So,

`y' = (cot ((2x)^(1/2)))'`

`y'=-csc^2((2x)^(1/2)) * 1/2 (2x)^(-1/2)*(2x)'`

`y'=-csc^2((2x)^(1/2)) * 1/2 (2x)^(-1/2)*2`

`y'=-csc^2(sqrt(2x)) * (2x)^(-1/2)`

`y'=-(csc^2(sqrt(2x)) )/(2x)^(1/2)`

`y'=-(csc^2(sqrt(2x)) )/sqrt(2x)`

Hence, the derivative is `y'=-(csc^2(sqrt(2x)) )/sqrt(2x)` ).

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