# How do you find the derivative of #y = (1/3)^(x^2)#?

Take the natural logarithm of both sides.

Use laws of logarithms to simplify.

Differentiate using implicit differentiation and the product rule.

Hopefully this helps!

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To find the derivative of ( y = (1/3)^{x^2} ), you can use the chain rule. First, take the natural logarithm of both sides to simplify the expression. Then, differentiate implicitly with respect to ( x ) and solve for ( \frac{dy}{dx} ). The derivative of ( y ) with respect to ( x ) is ( \frac{dy}{dx} = -2x (\ln(1/3)) (1/3)^{x^2} ).

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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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