# How do you take the derivative of #tan^ -1(3x^2)#?

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To take the derivative of ( \tan^{-1}(3x^2) ), you use the chain rule. The derivative of ( \tan^{-1}(u) ) with respect to ( x ) is ( \frac{1}{1+u^2} \frac{du}{dx} ). Here, ( u = 3x^2 ). Therefore, the derivative of ( \tan^{-1}(3x^2) ) with respect to ( x ) is ( \frac{1}{1+(3x^2)^2} \times \frac{d}{dx}(3x^2) ). Differentiating ( 3x^2 ) with respect to ( x ) yields ( 6x ). So, the final answer is ( \frac{6x}{1+9x^4} ).

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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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