# Math Help - first and second derivatives of a function

1. ## first and second derivatives of a function

can anyone help me finding first and second derivatives of these functions?

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

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

3) y=tan x- x i got up to 2 sec^2xtanx

4) y=ln (x^2+1)

thanks lots

2. Originally Posted by katieeej
can anyone help me finding first and second derivatives of these functions?

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

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

3) y=tan x- x i got up to 2 sec^2xtanx

4) y=ln (x^2+1)

thanks lots
#1 ...

$
\frac{d}{dx} \ln(u) = \frac{1}{u} \cdot \frac{du}{dx}
$

#2 ... chain rule

$
\frac{d}{dx} (u)^{\frac{1}{2}} = \frac{1}{2}(u)^{-\frac{1}{2}} \cdot \frac{du}{dx}
$

# 3 ...

$
\frac{d}{dx} (\tan{x} - x) = \sec^2{x} - 1 = \tan^2{x}
$

#4 ... use the rule given for #1.