How do you find the derivative of #x^(3/x)#?
use logs cos that's ugly!
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To find the derivative of ( x^{\frac{3}{x}} ), we use logarithmic differentiation. Let ( y = x^{\frac{3}{x}} ). Taking the natural logarithm of both sides gives ( \ln(y) = \frac{3}{x} \ln(x) ). Differentiate implicitly with respect to ( x ) and solve for ( \frac{dy}{dx} ) to find the derivative. After differentiation and simplification, the derivative is ( \frac{dy}{dx} = x^{\frac{3}{x}} \left( \frac{3}{x^2} - \frac{3 \ln(x)}{x^2} \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.
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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