# How do you differentiate #f(x) = arcsin(2x + 1)#?

The final answer is

This is found using the standard result for differentiating arcsine, and the chain rule.

Solution

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To differentiate ( f(x) = \arcsin(2x + 1) ), we apply the chain rule. The derivative of ( \arcsin(u) ) is ( \frac{1}{\sqrt{1 - u^2}} ), and then we multiply by the derivative of the inner function. In this case, the inner function is ( 2x + 1 ). So, the derivative of ( f(x) ) with respect to ( x ) is:

[ f'(x) = \frac{1}{\sqrt{1 - (2x + 1)^2}} \cdot (2) ]

Simplifying this expression gives the derivative of ( f(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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