# What is the first differential of #y= e^sinsqrtx# ?

Applying the chain rule:

Applying the chain rule again:

Applying the power rule:

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The first differential of ( y = e^{\sin(\sqrt{x})} ) is:

[ \frac{dy}{dx} = \frac{d}{dx} \left( e^{\sin(\sqrt{x})} \right) = e^{\sin(\sqrt{x})} \cdot \frac{d}{dx} \left( \sin(\sqrt{x}) \right) ]

Using the chain rule and the derivative of (\sin(\sqrt{x})), we get:

[ \frac{dy}{dx} = e^{\sin(\sqrt{x})} \cdot \cos(\sqrt{x}) \cdot \frac{1}{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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