y=-1/sqrt(x^2+1) , then dy/dx=

A. x/(x^2+1)^1/2
B. x/(x^2+1)^3/2
C. -x/(x^2+1)^1/2
D. -x/(x^2+1)^3/2
E. x/(x^2+1)

I got B.

Yes, B is correct, again using chain rule.

y = -1(x^2+1)^(-1/2)

y' = 1/2 (x^2+1)^(-3/2) (2x)
= x/(x^2+1)^(3/2)

you are correct

you can always check your answer at wolframalpha.com:

http://www.wolframalpha.com/input/?i=derivative+-1%2Fsqrt%28x%5E2%2B1%29

To find the derivative of the given function y = -1/sqrt(x^2 + 1), we can use the quotient rule. The quotient rule states that if we have a function of the form y = f(x)/g(x), where f(x) and g(x) are differentiable functions, then the derivative is given by:

dy/dx = (g(x)*f'(x) - f(x)*g'(x)) / (g(x))^2

In this case, f(x) = -1 and g(x) = sqrt(x^2 + 1). Let's calculate the derivatives:

f'(x) = 0 (since -1 is a constant value)
g'(x) = (1/2)*(x^2 + 1)^(-1/2)*(2x) = x / sqrt(x^2 + 1)

Now we can substitute these values into the quotient rule formula:

dy/dx = (sqrt(x^2 + 1)*0 - (-1)*(x/sqrt(x^2 + 1))) / (sqrt(x^2 + 1))^2
dy/dx = x / (x^2 + 1)

Therefore, the correct answer is E.