WEBVTT
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so this function that we have, we want to
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take the derivative of it. As we see,
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derivatives are going to be incredibly useful when determining the
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rate of change within a function. Determining the slope
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of tangent lines so grows are the one of the
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bases of Oculus. So it's important that we know
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how to do it regardless of what function we're using
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. And we see that functions have their own special
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properties. So, for example, the derivative of
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why or the derivative of inverse tangent? Well,
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give us something of the form 1/1. Plus you
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squared where you is, what, on the inside
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. So what we'll have here is 1/1 plus X
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squared squared, so that would just give us X
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to the fourth. Then, since we're doing a
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general, we need to make sure we multiply it
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by the derivative of the actual inner part, and
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we know that that's going to be two X.
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So this is gonna be X squared. So we
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know that that's right Here is gonna be two x
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So our final answer for why prime the derivative of
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the function is going to be two x over one
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plus X to the fourth best. We have our
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answer. And we know that this is the derivative
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of the function. We could even graph this.
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Um, we could graphic here. We see this
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is the graph we have, and then the derivative
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of it. We could just call. Why?
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We see that this is the derivative of that function
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. Um, based on how we solve for knowing
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the properties of the inverse tangent function.