Second derrivative from cain rule

[curlybit89]

I'm not sure if the various rules (chain, quotient, product) have an order of operations but I am a little confused here.

Found the derrivative of g(h(x)) where g = sqrt(x) and h = 1 + x^2

f ' x = (x) / (sqrt( 1 + x^2 ) )

Finding the second derivative should be simple enough, quotient using the derrivative of f(x) in the denominator?

I'm not able to compute (1) / ((1 + x ^ 2)^3/2)

Specifically, i'm not sure how to combine terms from the quotient rule:

(1)(sqrt(1+x^2)) - (x)(x / sqrt(1+x^2) ALL OVER sqrt(1+x^2)^2

 

[mmm4444bot]

Specifically, i'm not sure how to combine terms from the quotient rule:

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

\(\displaystyle \frac{\frac{\sqrt{1 \;+\;x^2}}{1} \;-\; \frac{x^2}{\sqrt{1 \;+\;x^2}}}{(\sqrt{1 \;+\;x^2})^2} \;=\; \frac{\frac{\sqrt{1 \;+\;x^2}}{\sqrt{1 \;+\; x^2}} \cdot \frac{\sqrt{1 \;+\;x^2}}{1} \;-\; \frac{x^2}{\sqrt{1 \;+\;x^2}}}{(\sqrt{1 \;+\;x^2})^2} \;=\; \frac{\frac{1 \;+\; x^2 - x^2}{\sqrt{1 \;+\;x^2}}}{(\sqrt{1 \;+\;x^2})^2} \;=\; \frac{1}{\sqrt{1 \;+\;x^2}} \cdot \frac{1}{(\sqrt{1 \;+\;x^2})^2} \;=\; \frac{1}{(1 \;+\; x^2)^{3/2}}\)