# What is the derivative of #tan^(-1)(x^2 y^5)#?

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The derivative of ( \tan^{-1}(x^2y^5) ) with respect to ( x ) is given by:

[ \frac{d}{dx} \left( \tan^{-1}(x^2y^5) \right) = \frac{10x^3y^5}{1 + x^4y^{10}} ]

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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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