richyw 3 years ago having a little bit of trouble remembering how to do the differential.

1. richyw

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 $$\frac{dk}{dt}$$.

2. richyw

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

3. richyw

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?

4. eseidl

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

5. richyw

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

6. richyw

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

7. eseidl

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

8. richyw

alright thanks a lot. I really appreciate it.

9. eseidl

I get:$e^{t^3+t^2+t+3}(3t^2+2t+1)$

10. eseidl

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

11. richyw

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