How do you differentiate #f(x)= ln(tanxx^2) #?
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To differentiate ( f(x) = \ln(\tan(x)  x^2) ), you would use the chain rule and the derivative rules for logarithmic and trigonometric functions:

Differentiate the outer function (\ln(u)) with respect to (u), where (u = \tan(x)  x^2), to get (\frac{1}{u}).

Multiply by the derivative of the inner function, which is obtained by applying the chain rule. The derivative of (\tan(x)) is (\sec^2(x)), and the derivative of (x^2) is (2x).

Therefore, the derivative of (f(x)) is:
[ f'(x) = \frac{1}{\tan(x)  x^2} \left(\sec^2(x)  2x\right) ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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