# How do you differentiate #y = lnx^2#?

Just to show the versatility of calculus, we can solve this problem through implicit differentiation.

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To differentiate ( y = \ln(x^2) ), you can use the chain rule. The chain rule states that if you have a function inside another function, you differentiate the outer function first, then multiply by the derivative of the inner function.

The derivative of ( \ln(u) ) with respect to ( u ) is ( \frac{1}{u} ), and the derivative of ( x^2 ) with respect to ( x ) is ( 2x ).

So applying the chain rule:

[ \frac{dy}{dx} = \frac{1}{x^2} \cdot 2x ]

[ \frac{dy}{dx} = \frac{2x}{x^2} ]

[ \frac{dy}{dx} = \frac{2}{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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