Chain Rule Exercise: Find dg/dx + dg/dy

Thread starter tsangz
Start date Nov 8, 2012
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Chain Chain rule Exercise

In summary, the chain rule is a formula used in calculus to calculate the derivative of a composite function. To apply the chain rule in finding dg/dx + dg/dy, you first need to identify the inner and outer functions of the composite function and then take the derivative of each function with respect to x and y. The purpose of finding dg/dx + dg/dy is to calculate the rate of change of a function with respect to two variables. The chain rule can also be used for functions with more than two variables by taking the partial derivatives with respect to each variable. Common mistakes to avoid when using the chain rule include forgetting to multiply the derivatives and mixing up the order of the variables. It is important to carefully follow the steps

Nov 8, 2012

tsangz

Homework Statement

Suppose g(x,y)=f(x-y,y-s)

Homework Equations

Nothing else

The Attempt at a Solution

Find dg/dx + dg/dy

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Nov 8, 2012

STEMucator

Homework Helper

Hmm I believe this exercise would be easier if you let r = x-y and p = y-s.

Related to Chain Rule Exercise: Find dg/dx + dg/dy

1. What is the chain rule?

The chain rule is a formula used in calculus to calculate the derivative of a composite function. It states that the derivative of a composite function is equal to the derivative of the outer function multiplied by the derivative of the inner function.

2. How do you apply the chain rule in finding dg/dx + dg/dy?

To apply the chain rule in finding dg/dx + dg/dy, you first need to identify the inner and outer functions of the composite function. Then, take the derivative of the outer function with respect to x and multiply it by the derivative of the inner function with respect to x. Next, take the derivative of the outer function with respect to y and multiply it by the derivative of the inner function with respect to y. Finally, add the two results together to get dg/dx + dg/dy.

3. What is the purpose of finding dg/dx + dg/dy?

Finding dg/dx + dg/dy allows us to calculate the rate of change of a function with respect to two variables, x and y, at the same time. This is useful in many fields of science, including physics, engineering, and economics.

4. Can the chain rule be used for functions with more than two variables?

Yes, the chain rule can be extended to functions with more than two variables. In this case, the derivative would be taken with respect to each variable separately, and all the partial derivatives would be multiplied together.

5. Are there any common mistakes to avoid when using the chain rule?

One common mistake to avoid when using the chain rule is to forget to multiply the derivative of the outer function by the derivative of the inner function. Another mistake is to mix up the order of the variables when taking the partial derivatives. It is important to carefully follow the steps of the chain rule to avoid these errors.