`y = ln(sqrt(x^2 - 4))` Find the derivative of the function.

Expert Answers

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First, use the formula:

`(lnu)'= 1/u*u'`

Applying that formula, the derivative of the function will be:

`y' =1/sqrt(x^2-4) * (sqrt(x^2-4))'`

To take the derivative of the inner function, express the radical in exponent form.


Then, use the formula:

`(u^n)'=n*u^(n-1) * u'`

So, y' will become:

`y'=1/sqrt(x^2-4) * 1/2(x^2-4)^(-1/2)*(x^2-4)'`

To take the derivative of the innermost function, use the formulas:


`(c)' = 0`

Applying these two formulas, y' will become:

`y'=1/sqrt(x^2-4) *1/2(x^2-4)^(-1/2)*(2x-0)`

Simplifying it will result to:






Therefore, the derivative of the given function is `y'=x/(x^2-4)` . 

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