# How do you differentiate #y = x ^ sqrt(x)#?

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To differentiate y = x ^ sqrt(x), you can use the chain rule. The derivative is:

dy/dx = (sqrt(x) * x^(sqrt(x) - 1)) + (x^(sqrt(x)) * (1/(2*sqrt(x))))

Simplified, this becomes:

dy/dx = sqrt(x) * x^(sqrt(x) - 1) + x^(sqrt(x))/(2*sqrt(x))

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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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