Differentiating a function

**factory1o1** · May 30th 2012, 05:15 PM

Its been sometime since I've taken a math course and most of the rules have slipped me.. I got some of the basics down on derivatives but i can't seem to work through these 2 problems. on prob 1 i get to 1/((e^2x)+5) but i know you have to keep it going.. on number 2 im just crushed

i THINK (x/(e^3x))^1/2 is the start

1.. g(x)=ln((e^2x)+5)

2.. t(x)=√(x/(e^3x))

**skeeter** · May 30th 2012, 06:15 PM

#1 ... $\frac{d}{dx} \ln(u) = \frac{1}{u} \cdot \frac{du}{dx} \, \,$ or $\, \, \frac{u'}{u}$ in simpler form

$\frac{d}{dx} \ln(e^{2x}+5) = \frac{1}{e^{2x}+5} \cdot 2e^{2x} = \frac{2e^{2x}}{e^{2x}+5}$

#2 is messy ...

$t(x) = \sqrt{\frac{x}{e^{3x}}} = \left(\frac{x}{e^{3x}}\right)^{1/2}$

$t'(x) = \frac{1}{2}\left(\frac{x}{e^{3x}}\right)^{-1/2} \cdot \left[\frac{e^{3x} - x \cdot 3e^{3x}}{(e^{3x})^2}\right]$

$t'(x) = \sqrt{\frac{e^{3x}}{x}} \cdot \frac{1 - 3x}{2e^{3x}}$

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