How to Differentiate Exponential Functions with Multiple Variables?

[andrey21]

Differentiate the following:

u = 2 (x-t² / 3)e^t/3

Here is my attempt

I have to find du/dx and du/dt

du/dx = 2 (x-t² / 3)e^t/3

du/dt = -4t/9 (x-t² / 3)e^t/3

 

[Unit]

It would help if you wrote u as 2xe^t/3 - (2/3)t²e^t/3. Since u is a function of both t and x, you will have to use the chain rule in your derivatives.

For example, if v = 3m², then dv/dx = d/dx (3m²) = d/dm (3m²) (dm/dx) = 6m dm/dx.

 

[andrey21]

Ok so from what you have said:

u = 2xe^t/3 - 2/3 t²e^t/3

du/dx = 2/ e ^t/3

du/dt = 2/3 xe ^t/3 - 4/9 t e ^t/3

 

[Quinzio]

Ok du/dx
There are errors in du/dt

 

[andrey21]

Ah yes I need to adopt the product rule on:

-2/3 t² e ^t/3