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having a little bit of trouble remembering how to do the differential.
 one year ago
 one year ago
having a little bit of trouble remembering how to do the differential.
 one year ago
 one year ago

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richywBest ResponseYou've already chosen the best response.0
so I have \(k(x,y,z)=e^{x^2+y^2+z^2}\) where \(x=\sqrt{t+1},\;y=\sqrt{t^2+1},\:z=\sqrt{t^3+1}\) . Now i need to find \(\frac{dk}{dt}\).
 one year ago

richywBest ResponseYou've already chosen the best response.0
to do this do I just say\[\frac{dk}{dt}=\frac{dk}{dx}\frac{dx}{dt}+\frac{dk}{dy}\frac{dy}{dt}+\frac{dk}{dz}\frac{dz}{dt}\]
 one year ago

richywBest ResponseYou've already chosen the best response.0
I am getting an answer of \[\frac{dk}{dt}=2e^{t^3+t^2+t+3}\left(3t^2+2t+1\right)\] is this correct, and does anyone know how to check this on wolfram, or opensource math software?
 one year ago

eseidlBest ResponseYou've already chosen the best response.1
The formula for the total differential is correct, as long as the dk/dx,etc terms are partial derivatives.
 one year ago

richywBest ResponseYou've already chosen the best response.0
yeah sorry I didn't want to type "partial" \(\partial\) in the latex that many times :)
 one year ago

richywBest ResponseYou've already chosen the best response.0
thanks a lot. can anyone confirm this is the correct answer?
 one year ago

eseidlBest ResponseYou've already chosen the best response.1
this one is super tedious...give me a minute I'll do it with pen and paper...
 one year ago

richywBest ResponseYou've already chosen the best response.0
alright thanks a lot. I really appreciate it.
 one year ago

eseidlBest ResponseYou've already chosen the best response.1
I get:\[e^{t^3+t^2+t+3}(3t^2+2t+1)\]
 one year ago

eseidlBest ResponseYou've already chosen the best response.1
Your factor of two should cancel when you differentiate the square root term (which gives you a 2 in the denominator)...
 one year ago

richywBest ResponseYou've already chosen the best response.0
thanks a lot! I see I made a basic calculus mistake but am glad I remember this stuff!
 one year ago
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