# How do you differentiate #x^sqrt5+sqrt(5x)#?

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To differentiate (x^{\sqrt{5}} + \sqrt{5x}), apply the chain rule and power rule separately to each term. The derivative of (x^{\sqrt{5}}) is (\sqrt{5} \cdot x^{\sqrt{5}-1}), and the derivative of (\sqrt{5x}) is (\frac{1}{2\sqrt{5x}} \cdot 5). So, the derivative of (x^{\sqrt{5}} + \sqrt{5x}) with respect to (x) is (\sqrt{5} \cdot x^{\sqrt{5}-1} + \frac{5}{2\sqrt{5x}}).

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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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