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Problem 50 Easy Difficulty

Find the derivative of the function. Simplify where possible.
$ y = \tan^{-1} (x^2) $

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Video Transcript

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