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romeo6
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If I have two functions, f(x,y,z) and g(x,y,z), do I use the chain rule to calculate df/dg?
e.g. df/dg=df/dx df/dy df/dz
Cheers!
Romeo
e.g. df/dg=df/dx df/dy df/dz
Cheers!
Romeo
mjpam said:Are you really trying to find the derivative of one function with respect to the other function?
romeo6 said:Is that not possible?
romeo6 said:But if f is a function for (x,y,z) and g is a function of (x,y,z) then surely that's possible. Probably I'm wrong if I have to ask about it.
Hey, ex and x+1 are both function of x. What is the derivative of ex with respect to x+1?romeo6 said:But if f is a function for (x,y,z) and g is a function of (x,y,z) then surely that's possible. Probably I'm wrong if I have to ask about it.
mjpam said:Is there a way that you can justify this?
I'm just wondering if you have more than your intuition.
romeo6 said:You're right - just intuition. Which is probably failing me.
Amok said:Are you guys ignoring my posts on purpose :( ?
Amok said:Didn't I make my point explicitly? I'm not trying to sound like a douche or anything, I actually thought the same thing as romeo6 when I first red your question.
Amok said:Did you take a look at my first post in this thread?
mjpam said:I did. I just missed when I was reviewing the thread. Sorry.
Amok said:If f is not a function g, then you derivative equals 0, if I'm not mistaken.
This really doesn't make much sense. You don't calculate the derivative of a function with respect to some other function, but you do calculate the derivative of a function with respect to one of its variables. Here g is a function, not a variable, so df/dg is nonsensical.romeo6 said:If I have two functions, f(x,y,z) and g(x,y,z), do I use the chain rule to calculate df/dg?
e.g. df/dg=df/dx df/dy df/dz
Mark44 said:This really doesn't make much sense. You don't calculate the derivative of a function with respect to some other function, but you do calculate the derivative of a function with respect to one of its variables. Here g is a function, not a variable, so df/dg is nonsensical.
romeo6 said:If I have two functions, f(x,y,z) and g(x,y,z), do I use the chain rule to calculate df/dg?
e.g. df/dg=df/dx df/dy df/dz
Cheers!
Romeo
Amok said:If f is not a function g, then you derivative equals 0, if I'm not mistaken.
mjpam said:What is your mathematical background? Are you learning (or teaching yourself) calculus right now?
Mark44 said:This really doesn't make much sense. You don't calculate the derivative of a function with respect to some other function, but you do calculate the derivative of a function with respect to one of its variables. Here g is a function, not a variable, so df/dg is nonsensical.
For another thing, both functions here have multiple variables, so instead of df/dx, df/dy, and df/dz, you would be working with partial derivatives,
[tex]\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \text{and} \frac{\partial f}{\partial z}[/tex]
Other notation for these partials is fx, fy, and fz.
chiro said:Have you done Calculus III (Multivariable calculus)?
romeo6 said:I've taken plenty of calculus (believe it or not), it's been a few years now though, and I've not used it for a while.
mjpam said:Why does it not makes sense to define a derivative of a function with respect to another function?
I disagree strongly with this- you always take the derivative of a function with respect to another function! In basic Calculus , of course, that second function is the identity function, x. But asking for the derivative of f with respect to g is just asking how fast f changes relative to g. If f and g are functions of the single variable, x, then, by the chain ruleMark44 said:This really doesn't make much sense. You don't calculate the derivative of a function with respect to some other function, but you do calculate the derivative of a function with respect to one of its variables. Here g is a function, not a variable, so df/dg is nonsensical.
For another thing, both functions here have multiple variables, so instead of df/dx, df/dy, and df/dz, you would be working with partial derivatives,
[tex]\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \text{and} \frac{\partial f}{\partial z}[/tex]
Other notation for these partials is fx, fy, and fz.
The Chain Rule is a mathematical rule that is used to calculate the derivative of a composite function. In other words, it allows us to find the rate of change of a function that is made up of multiple smaller functions. This is important because many real-world problems involve complex functions that cannot be easily differentiated without the use of the Chain Rule.
To use the Chain Rule, you must first identify the inner and outer functions of the composite function. Then, you can use the formula df/dg = (df/dx)(dx/dg) to calculate the derivative. This involves finding the derivatives of the individual functions and plugging them into the formula.
Sure! Let's say we have the function f(x) = sin(2x). The inner function is 2x and the outer function is sin(x). Using the Chain Rule formula, we can calculate df/dg = (df/dx)(dx/dg) = (2cos(2x))(2) = 4cos(2x). This gives us the derivative of f(x) with respect to g.
Yes, there are a few common mistakes to watch out for. One is forgetting to find the derivative of the inner function, or using the wrong derivative for the inner function. Another mistake is not properly simplifying the final answer, which can lead to incorrect results. It's important to carefully follow the steps and double check your work when using the Chain Rule.
The best way to practice and improve your skills is to work on a variety of problems that involve composite functions. You can find practice problems online or in textbooks, or create your own problems to solve. It's also helpful to review the steps and formulas for the Chain Rule regularly to keep them fresh in your mind.