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Name: 1 Class: Use the Chain Rule to find Date: dz if z x LN x + 5y, x sin t, and y cos t. () DT a. dz DT x + LN (x + 5y) x + 5y cos t x (sin t) x + 5y b. dz DT x + LN (x + 5y) x + 5y sin t + x (cos
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How to fill out use form chain rule
How to fill out and use the chain rule:
01
Identify the function and variable of the outermost function in the chain rule expression.
1.1
This will be the function whose derivative needs to be calculated.
02
Differentiate the outermost function with respect to its variable.
2.1
Apply the appropriate derivative rules and techniques to find the derivative of the outermost function.
03
Identify the function and variable inside the outermost function.
3.1
This will be the inner function that was used to compose the outer function.
04
Differentiate the inner function with respect to its variable.
4.1
Use the chain rule to differentiate the inner function obtained in the previous step.
05
Multiply the derivative of the outermost function (from step 2) by the derivative of the inner function (from step 4).
5.1
This will give you the derivative of the composite function obtained by chaining the two functions together.
06
Simplify and express the final derivative in terms of the original variables.
6.1
Combine terms and simplify the expression if necessary to obtain the final derivative result.
Who needs to use the chain rule?
The chain rule is an essential tool in calculus and is primarily used by students, academics, and professionals in various fields. Here are some examples of who may need to use the chain rule:
01
Mathematics students studying calculus, particularly in topics such as differential calculus and optimization.
1.1
The chain rule is a fundamental concept in calculus and is extensively used to find derivatives of composite functions.
02
Engineers and scientists dealing with mathematical modeling and analysis.
2.1
When analyzing complex systems or developing mathematical models, the chain rule helps in finding the relationships between variables and their rates of change.
03
Economists and finance professionals working with optimization and marginal analysis.
3.1
The chain rule allows for precise calculations of marginal rates of substitution, marginal propensities, and other relevant economic variables.
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