# How do you find the derivative #e^(x+y) + e^2x +e^2y#?

If I have misunderstood your question, please accept my apology.

For each term, we will need the chain rule applied to the exponential function:

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To find the derivative of ( e^{x+y} + e^{2x} + e^{2y} ) with respect to ( x ), you can apply the chain rule and the rule for differentiating exponential functions. The derivative with respect to ( x ) is:

( \frac{d}{dx} \left( e^{x+y} + e^{2x} + e^{2y} \right) = e^{x+y} \cdot (1 + 1) + e^{2x} \cdot 2 + 0 )

( = e^{x+y} \cdot 2 + 2e^{2x} )

Similarly, to find the derivative with respect to ( y ), you would get:

( \frac{d}{dy} \left( e^{x+y} + e^{2x} + e^{2y} \right) = e^{x+y} \cdot (1 + 1) + 0 + e^{2y} \cdot 2 )

( = e^{x+y} \cdot 2 + 2e^{2y} )

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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.

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.

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.

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