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How do you differentiate #x / (x^2 + 1)^(1/2)#?

1 Answer

May 13, 2018

#d/dx ( x/(x^2+1)^(1/2)) =1/(x^2+1)^(3/2)#

Explanation:

Using the quotient rule:

#d/dx ( x/(x^2+1)^(1/2)) = ( (x^2+1)^(1/2) - x (2x)/(2(x^2+1)^(1/2)))/(x^2+1)#

#d/dx ( x/(x^2+1)^(1/2)) = (x^2 +1 -x^2)/(x^2+1)^(3/2)#

#d/dx ( x/(x^2+1)^(1/2)) =1/(x^2+1)^(3/2)#

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