# What is the derivative of #f(x)=log_4(e^x+3)# ?

First, we will rewrite the function in terms of natural logarithms, using the change-of-base rule:

Differentiating will require use of the chain rule:

Simplifying yields:

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To find the derivative of ( f(x) = \log_4(e^x + 3) ), apply the chain rule:

[ f'(x) = \frac{1}{\ln(4)} \cdot \frac{1}{e^x + 3} \cdot e^x ]

So, the derivative of ( f(x) ) is:

[ f'(x) = \frac{e^x}{\ln(4)(e^x + 3)} ]

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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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