How do you differentiate #y=e^(e^x)#?
If you are studying maths, then you should learn the Chain Rule for Differentiation, and practice how to use it:
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To differentiate ( y = e^{e^x} ), you can use the chain rule. The chain rule states that if you have a function within a function, you differentiate the outer function first, leaving the inner function unchanged, then multiply by the derivative of the inner function.
So, for ( y = e^{e^x} ):

Differentiate the outer function ( e^{e^x} ) with respect to ( x ). The derivative of ( e^u ) with respect to ( u ) is ( e^u ), so in this case, the derivative of ( e^{e^x} ) with respect to ( e^x ) is ( e^{e^x} ).

Now, differentiate the inner function ( e^x ) with respect to ( x ), which is ( e^x ).

Multiply the results of steps 1 and 2 together to get the final derivative.
So, ( \frac{dy}{dx} = e^{e^x} \cdot e^x = e^{e^x + x} ).
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
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