What is derivative of y =`sqrt(x^2+1)`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the derivative of the given function, hence, since the function is the result of composition of two functions, you need to use the chain rule, such that:

`y' = (sqrt(x^2 + 1))'*(x^2 + 1)'`

You ned to notice that you need to start to differentiate the square root and then you differentiate the radicand.

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

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

Reducing the duplicate factors yields:

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

Hence, evaluating the derivative of the given function, using the chain rule, yields `y' = x/(sqrt(x^2 + 1)).`