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I am trying to do a question for calculus. I am supposed to find a minimum time for something.. I know how to do the question but I am stuck on how to find the derivative of this function it really confuses me.
(sq. root 1^2+x^2)/3 + 3-x/5
I need to find dt/dx... and I am clueless on how to find this???
THANKS TONS!
robert Ihnot
May9-05, 10:52 PM
d\sqrt{Y}=\frac{dY}{2\sqrt{Y}} Now for Y = A+B, the rule is:
Y'=A'+B'. In the case of a form such as S/T, you can employ the rule:
d(S/T) =\frac{S'T-ST'}{T^2}
However, in the problem above we don't need to use that since: d(X/3) is just X'/3. Again in the case
\sqrt{\frac{1+x^2}{3}}=\frac{\sqrt{1+x^2}}{\sqrt3} which is simpler to work with.
James R
May10-05, 12:11 AM
To differentiate
t= \frac{\sqrt{1 + x^2}}{3}
put u=1 + x^2, then use the chain rule:
\frac{dt}{dx} = \frac{dt}{du} \frac{du}{dx}
Jameson
May10-05, 11:03 AM
Or pulling out constants might make it seem simpler.
\frac{1}{3}*\frac{d\sqrt{1+x^2}}{dx} etc...
HallsofIvy
May10-05, 11:36 AM
Most people find it easier to think of "square root" as "1/2 power". That is,
To find the derivative of \frac{\sqrt{1+x^2}}{3} + 3- \frac{x}{5}[/itex], write it as [tex]\frac{1}{3}(1+ x^2)^{\frac{1}{2}}+ 3- \frac{x}{5}[/itex]
Then the derivative is [itex]\frac{1}{3}\frac{1}{2}(1+ x^2)^{-\frac{1}{2}}{2x}- \frac{1}{5}
You Guys Are Awesome Thanks Sooo Much!!!
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