# How do you differentiate #y=(sin(3x))^(ln(x))#?

Begin by taking the log of both sides of the equation:

Notes:

In [B] the Product Rule is combined with the Chain Rule to determine the derivative of the right side.

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To differentiate ( y = (\sin(3x))^{\ln(x)} ), you can use the chain rule and the logarithmic differentiation. The derivative is ( y' = (\sin(3x))^{\ln(x)} \left( \frac{3\cos(3x)}{\sin(3x)} \ln(x) + \frac{\cos(3x)}{\sin(3x)} \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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