Derivative question

Sep 2009
37
1
Hi,

I'm having a little trouble with finding the derivative of this one. The fraction with the square root is giving me the trouble, I'm not sure if I should be using the quotient rule or the chain rule or the chain rule within the quotient rule.
Anyone able to clarify this for me?

Thanks
David

\(\displaystyle y=60-\frac{x}{5}+ \frac{\sqrt{100^2+x^2}}{3}\)
 
Jan 2010
354
173
Since the denominator of the fraction is a constant, it's easiest to merely factor out the constant. What I mean is:

\(\displaystyle \frac{d}{dx} \left[ \frac{\sqrt{100^2+x^2}}{3} \right]= \frac{1}{3} \cdot \frac{d}{dx} \left[ \sqrt{100^2+x^2} \right]\)

At this point you should use the chain rule where \(\displaystyle u=100^2+x^2\) to give

\(\displaystyle \frac{1}{3} \cdot \frac{d}{du} \left[ u^{1/2} \right] \cdot \frac{d}{dx} \left[100^2+x^2 \right]\)

Does this answer your question?
 
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Reactions: Splint
Sep 2009
37
1
Thanks Drumist, it took a but to follow at first but I've got it now. Cheers