How do you find the derivative of #y= x arctan 2x - (1/4) ln (1+4x^2)#?
Using the product rule and the chain rule:
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To find the derivative of ( y = x \arctan(2x) - \frac{1}{4} \ln(1+4x^2) ), you can use the sum and chain rules of differentiation. The derivative is:
[ y' = \arctan(2x) + \frac{x}{1+4x^2} - \frac{x}{1+4x^2} ]
Simplified, the derivative is:
[ y' = \arctan(2x) + \frac{x}{1+4x^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.
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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