# How do you differentiate #(1+x)^(1/x)#?

The function:

has only positive values, so we can take its logarithm:

Differentiate now the equation above:

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To differentiate (1+x)^(1/x), you can use logarithmic differentiation. Let y = (1+x)^(1/x). Take the natural logarithm of both sides. Then differentiate implicitly with respect to x and solve for dy/dx. The result is dy/dx = (1+x)^(1/x) * [(1/x^2) * (1-ln(1+x)) + (ln(1+x))/(x^2)].

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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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