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Evaluate the derivatives of the given functions for the given values of $x$. Use the product rule. Check your results using the derivative evaluation feature of a calculator.$$y=\left(2 x^{2}-x+1\right)\left(4-2 x-x^{2}\right), x=-3$$

Calculus 1 / AB

Chapter 23

The Derivative

Section 6

Derivatives of Products and Quotients of Functions

Derivatives

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All right. We're going to evaluate dy dx when X equals uh negative three. But I double checked, I was about to write down three. And what we have is this product that consists of two X squared minus X plus one times the quantity there's your product Uh 4 -2 x minus x squared. So the way to go about this problem is to identify the product as already mentioned. So what we have to do is take the drift of of the left side. 1st you leave the right side alone and then plus now you leave the left side alone. Okay? And multiply by the derivative of the right side, which would be -2 -2 x. So from here there's a lot of plugging in but I think you can do this without. A calculator is four times negative through being negative, 12 -1 is negative. 13 Plugging in -3. Here and here. I'm yet to do this math. May Like writing out plus six minus nine because remember when you square negative is positive, so that negative is still there, So 10 -9 would be one. Yeah, let's see, negative three here, negative three here, negative three here. So it'll be nine times two is 18. That becomes plus three plus one, so 22. And then uh negative two plus six if my math is correct that before. So it looks like I have negative 13 plus 88. So 88 -13 Give me an answer of 75. Yeah. And that appears to be correct. So let's circle it. Move on. Yeah.

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