Question

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

Answer 1

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 \(\frac{dk}{dt}\).

Answer 2

to do this do I just say\[\frac{dk}{dt}=\frac{dk}{dx}\frac{dx}{dt}+\frac{dk}{dy}\frac{dy}{dt}+\frac{dk}{dz}\frac{dz}{dt}\]

Answer 3

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 open-source math software?

Answer 4

The formula for the total differential is correct, as long as the dk/dx,etc terms are partial derivatives.

Answer 5

yeah sorry I didn't want to type "partial" \(\partial\) in the latex that many times :)

Answer 6

thanks a lot. can anyone confirm this is the correct answer?

Answer 7

this one is super tedious...give me a minute I'll do it with pen and paper...

Answer 8

alright thanks a lot. I really appreciate it.

Answer 9

I get:\[e^{t^3+t^2+t+3}(3t^2+2t+1)\]

Answer 10

Your factor of two should cancel when you differentiate the square root term (which gives you a 2 in the denominator)...

Answer 11

thanks a lot! I see I made a basic calculus mistake but am glad I remember this stuff!