# What is the derivative of #x^sin(x)#?

After the chain rule

we get

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The derivative of ( x^{\sin(x)} ) with respect to ( x ) is given by:

[ \frac{d}{dx} \left( x^{\sin(x)} \right) = x^{\sin(x)} \left( \frac{d}{dx}(\sin(x) \ln(x)) + \frac{\sin(x)}{x} \right) ]

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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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