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Question 1022092: Hi! Please help me with this question.
Differentiate y= sqrtx / (x^2+1) using the quotient rule
My work:
f'(x) =((x^2+1)(x^(1/2))' - (x^(1/2))(x^2+1)')/(x^2+1)^2
= ((x^2+1)(1/2x^(-1/2)) - (x^(1/2))(2))/ (x^2+1)^2
= (1/2x^(5/2) + 1/2x^(-1/2)-2x^(1/2))/ (x^2+1)^2
I can't seem to get the answer which is (1-3x^2)/((2sqrtx)(x^2+1)^2)
Thank you!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Look at the numerator first
it is (x^2+1)*(1/2 sqrt (x))- sqrt(x)*2x
Now put this over a common denominator of 2 sqrt(x). That means multiplying the second term by 2(sqrt(x)), and that will be 4x^2.
The common denominator of 2 sqrt (x) goes into the denominator with (x^2+1)^2.
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Now, the numerator is (x^2+1)-4x^2, the common denominator now part of the answer denominator.
That is 1-3x^2.
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