Partial derivative of T(x, y, z) = 200e^(−x²−3y²−9z²)

[killersanta]

Homework Statement

T(x, y, z) = 200e^(−x^2−3y^2−9z^2 )
I'm not sure how to get the derivative in terms of x,y or z.

The Attempt at a Solution

For x: -200x^2e^(−x^2−3y^2−9z^2 )(-2x)? Is this right? Probably not, how do i do it?

 

[Mark44]

Homework Statement

T(x, y, z) = 200e^(−x^2−3y^2−9z^2 )
I'm not sure how to get the derivative in terms of x,y or z.

The Attempt at a Solution

For x: -200x^2e^(−x^2−3y^2−9z^2 )(-2x)? Is this right? Probably not, how do i do it?

This is not quite the correct partial derivative of T with respect to x. That's the terminology that is usually used.

The corrected version is -200e^(−x^2−3y^2−9z^2 )(-2x)

The notation can appear in two forms:
$$\frac{\partial T}{\partial x}$$
or
T_x

 

[killersanta]

thank you!

 

[Mark44]

Do you understand why that x² factor you had shouldn't be there?

 

[killersanta]

Do you understand why that x² factor you had shouldn't be there?

No, I thought you pulled it down? Why?