# `f(x) = (x^2)/(2sqrt(x) + 1)` Use the Quotient Rule to find the derivative of the function.

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Expert Answers

mathace | Certified Educator

Given: `f(x)=(x^2)/(2sqrt(x)+1)=(x^2)/(2x^(1/2)+1)`

Find the derivative using the Quotient Rule.

`=[(2sqrt(x)+1)(2x)-(x^2)(x^(-1/2))]/[(2sqrt(x)+1)^2]`

`=(4x^(3/2)+2x-x^(3/2))/[(2sqrt(x)+1)^2]`

`=(3x^(3/2)+2x)/[(2sqrt(x)+1)^2]`

`=[x(3x^(1/2)+2)]/[(2sqrt(x)+1)^2]`

`=[x(3sqrt(x)+2)]/[(2sqrt(x)+1)^2]`