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How do you find the derivative of #u=e^(e^x)#?

Answer 1

Christopher Agresta

Apply the chain rule.

The chain rule states that

#"d"/("d"x)"f"("g"(x))="f"'("g"(x))*"g"'(x)#.

Let #"f"(x) = e^(x)#, #"g"(x)=e^x#.

Then,

#"d"/("d"x) e^(e^(x))=e^x*e^(e^(x))#.

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Answer 2

Charles Arocha

To find the derivative of ( u = e^{e^x} ), you can use the chain rule. The chain rule states that if you have a function ( f(g(x)) ), then its derivative is ( f'(g(x)) \cdot g'(x) ). In this case, ( u ) is a composition of two functions: ( e^{e^x} ).

First, find the derivative of the outer function ( e^x ), which is simply ( e^x ). Then, find the derivative of the inner function ( e^x ), which is also ( e^x ).

Now, multiply these derivatives together:

[ \frac{du}{dx} = e^{e^x} \cdot e^x = e^{e^x + x} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.