# Thread: find the second derivative of...

1. ## find the second derivative of...

Find the second derivative of f(x)= sq rt(x^2 + 1)

I think the first derivative is x(x^2 + 1)^-1/2

But, I don't know how to find the derivative of that?

A) x/sq rt (x^2 + 1)

B) sq rt(x^2 + 1) - 1/2(x^2 + 1)^-1/2

C) 2x(sq rt(x^2 + 1) + 1/2(x^2 + 1)^-1/2

D) 1/sq rt((x^2 + 1)^3)

2. Originally Posted by obsmith08
Find the second derivative of f(x)= sq rt(x^2 + 1)

I think the first derivative is x(x^2 + 1)^-1/2

But, I don't know how to find the derivative of that?

A) x/sq rt (x^2 + 1)

B) sq rt(x^2 + 1) - 1/2(x^2 + 1)^-1/2

C) 2x(sq rt(x^2 + 1) + 1/2(x^2 + 1)^-1/2

D) 1/sq rt((x^2 + 1)^3)
Now apply the product rule, which states $\frac{\,d}{\,dx}\left[f\!\left(x\right)g\!\left(x\right)\right]=f\!\left(x\right)\frac{\,dg}{\,dx}+g\!\left(x\rig ht)\frac{\,df}{\,dx}$. Treat $x$ as $f\!\left(x\right)$ and $\left(x^2+1\right)^{-1}$ as $g\!\left(x\right)$.