first and second derivatives of a function

**katieeej** · March 6th 2009, 12:52 AM

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

**skeeter** · March 6th 2009, 04:19 AM

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.

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