Calculate Derivatives of f(x,y,z,t), g(x,y) & h(x,y,z)

  • Thread starter pointassist30
  • Start date
  • Tags
    Derivatives
In summary, the problem involves calculating the derivative of three functions with multiple variables. The suggested approach is to split the problem into parts and take the derivative of one variable at a time, assuming the other variables are constant. The specific method for taking the derivative is not specified and assistance is requested.
  • #1
pointassist30
1
0

Homework Statement



calculate the derivative of the following functions?

f(x,y,z,t) = (x-1)(2-y)z + (t^3 - 1)xyz
g(x,y) = 1/(1 + exp(-(ax + by + c))
h(x,y,z) = (x-1)^2 exp(x) + (y-2)^3 * z^3

The Attempt at a Solution



the way i was thinking was may be split the problem into multiple parts according to different variales. so if i have x,y,z in my problem...split into three parts and take derivative of one variable at a time. when taking a derivate, assume the other variables are constant.

not really sure how to do it though.

any help would be appreciated.

thanks.
 
Physics news on Phys.org
  • #2
pointassist30 said:
so if i have x,y,z in my problem...split into three parts and take derivative of one variable at a time. when taking a derivate, assume the other variables are constant
Thats exactly right, i.e.
[tex]
df(x,y) = \frac{\partial f(x,y)}{\partial x} dx + \frac{\partial f(x,y)}{\partial y} dy
[/tex]

So, if you have something like [tex]f(x,y) = x^2y + x + y[/tex] you get:
[tex]df(x,y) = (2xy + 1)dx + (x^2 + 1)dy [/tex]

When you take the derivative with respect to each variable, you pretend the other variables are all constant
 
  • #3
pointassist30 said:

Homework Statement



calculate the derivative of the following functions?
What do you mean by "the derivative" of a function of several variables? The partial derivatives or, as zhermes interpreted it, the differential?

f(x,y,z,t) = (x-1)(2-y)z + (t^3 - 1)xyz
g(x,y) = 1/(1 + exp(-(ax + by + c))
h(x,y,z) = (x-1)^2 exp(x) + (y-2)^3 * z^3

The Attempt at a Solution



the way i was thinking was may be split the problem into multiple parts according to different variales. so if i have x,y,z in my problem...split into three parts and take derivative of one variable at a time. when taking a derivate, assume the other variables are constant.

not really sure how to do it though.

any help would be appreciated.

thanks.
 

1. How do I calculate the derivative of a function with multiple variables?

To calculate the derivative of a function with multiple variables, you will need to use partial derivatives. This means taking the derivative with respect to one variable at a time while treating the other variables as constants. The resulting partial derivatives can then be combined to find the total derivative.

2. Can I use the chain rule to calculate derivatives of functions with multiple variables?

Yes, the chain rule can be applied to functions with multiple variables. When using the chain rule, each variable must be treated separately and the resulting partial derivatives must be multiplied together to obtain the total derivative.

3. Is there a specific order in which I should take the partial derivatives?

No, there is no specific order in which the partial derivatives must be taken. However, it is usually recommended to take the derivatives in an order that is most convenient or intuitive for the given function.

4. Can I use the product rule to calculate derivatives of functions with multiple variables?

Yes, the product rule can be applied to functions with multiple variables. When using the product rule, each variable must be treated separately and the resulting partial derivatives must be added together to obtain the total derivative.

5. Are there any special cases when calculating derivatives of functions with multiple variables?

Yes, there are some special cases that may require additional techniques when calculating derivatives of functions with multiple variables. These include functions with discontinuities, functions with non-continuous partial derivatives, and functions with implicit variables.

Similar threads

  • Calculus and Beyond Homework Help
Replies
2
Views
439
  • Calculus and Beyond Homework Help
Replies
8
Views
301
  • Calculus and Beyond Homework Help
Replies
6
Views
676
  • Calculus and Beyond Homework Help
Replies
13
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
489
  • Calculus and Beyond Homework Help
Replies
3
Views
559
  • Calculus and Beyond Homework Help
Replies
17
Views
1K
  • Calculus and Beyond Homework Help
Replies
23
Views
1K
Replies
1
Views
425
  • Calculus and Beyond Homework Help
Replies
3
Views
451
Back
Top