Learn the Chain Rule for Finding the Derivative of e^sec(x) | Homework Question

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The derivative of e^sec(x) is calculated using the chain rule. By letting u = sec(x) and y = e^u, the derivatives are found as du/dx = tan(x)sec(x) and dy/du = e^u. The final derivative is expressed as dy/dx = e^sec(x)tan(x)sec(x). The solution is confirmed as correct by participants in the discussion. This method effectively applies the chain rule to find the derivative of the given function.
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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)
 
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alpha01 said:

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)
Looks good to me :approve:
 
thanks
 

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