What is the derivative of #f(x)=e^(pix)*cos(6x)# ?
It looks a little complicated, but break it down into pieces that you know how to solve. On the highest level, we see a product of 2 functions, so you should be thinking product rule:
And we get the final answer by substituting:
and rearrange to get the answer on the first line.
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The derivative of f(x) = e^(pix) * cos(6x) with respect to x is -pie^(pix) * sin(6x) + 6e^(pix) * cos(6x).
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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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