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alpha01
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Homework Statement
derivative of esec(x)The Attempt at a Solution
u = sec(x)y = eu
du/dx = tan(x)sec(x)
dy/du = eu
dy/dx = dy/du * du/dx
= esec(x)tan(x)sec(x)
Learn the Chain Rule for Finding the Derivative of e^sec(x) | Homework Question
- Thread starter alpha01
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- Chain Chain rule
In summary, the chain rule is a mathematical rule used to find the derivative of a composite function. It involves multiplying the derivative of the outer function by the derivative of the inner function. A composite function is made up of two or more functions, with the output of one becoming the input of another. To use the chain rule for a function like e^sec(x), we first identify the inner and outer functions and then take the derivative of each and multiply them together. The chain rule is important because it simplifies finding the derivative of complicated functions and is widely used in various fields. An example of using the chain rule to find the derivative of e^sec(x) is to first take the derivative of e^x and then multiply it by
y = eu
du/dx = tan(x)sec(x)
dy/du = eu
dy/dx = dy/du * du/dx
= esec(x)tan(x)sec(x)
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Hootenanny
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Looks good to mealpha01 said:
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alpha01
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thanks
1. What is the chain rule?
The chain rule is a mathematical rule that allows us to find 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. What is a composite function?
A composite function is a function that is made up of two or more functions, where the output of one function becomes the input of another. In other words, the inner function is being applied to the output of the outer function.
3. How do I use the chain rule to find the derivative of e^sec(x)?
To find the derivative of e^sec(x), we use the chain rule by first identifying the inner and outer functions. The inner function is sec(x) and the outer function is e^x. We then take the derivative of the outer function, which is e^x, and multiply it by the derivative of the inner function, which is sec(x)tan(x). This gives us the derivative of e^sec(x) as e^sec(x)tan(x).
4. Why is the chain rule important?
The chain rule is important because it allows us to find the derivative of complicated functions by breaking them down into simpler functions. It is a fundamental rule in calculus and is used in many applications, such as optimization, physics, and engineering.
5. Can you provide an example of using the chain rule to find the derivative of e^sec(x)?
Yes, for example, if we have the function f(x) = e^sec(x), we can use the chain rule to find its derivative as follows:
f'(x) = e^sec(x) * sec(x)tan(x)
Where e^sec(x) is the outer function and sec(x) is the inner function. We first take the derivative of e^x, which is e^x, and then multiply it by the derivative of sec(x), which is sec(x)tan(x). Thus, the derivative of e^sec(x) is e^sec(x)tan(x).
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