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Find an equation for the tangent line to the graph at the specified value of $x .$$$y=\left(x-\frac{1}{x}\right)^{3}, x=2$$

$1135 x+16 y+216=0$

Calculus 1 / AB

Chapter 2

THE DERIVATIVE

Section 6

The Chain Rule

Functions

Limits

Derivatives

Differentiation

Continuous Functions

Applications of the Derivative

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eso these tangent line problems. You need to know your ex cornett, which they tell you. I mean called x one. Now you need to find your wife. Cornet, you need to find your slope. Um which the slope is the derivative when X equals two and a reason why you need this is in point slope form. Um, written like this I prefer this form. All you have to do is fill in the blanks. What's your M? What's your ex one with your Why one? Well, we already know the X one. We also know the equation they tell you is X minus one over X, uh, cubed. Well, if we plug to into this problem here and here, we get to minus one half, which I hope you know already is three halves. Well, if you cube that, you'll get three times. Three times three is 27/8. I just found the y coordinate. And now what we need is attributed of this. That's where the changeable comes into play and why they're doing it here, where you bring the three in front X minus one over X is now to the second power times that by ah, the derivative of the inside. Uh, which is one minus. Well, this is excellent at your first power. So you bring the native first in front X to the name of second power because you subtract one from that, you write it like that double check my math. What's nice? Those we plugged in to earlier, like, into this piece. So it's very similar because we did two minus one half, which is three halves. But now we're squaring that piece times one plus 1/4 cause two squared is four. And that's five force. So this is how I would do this, um, three times, three times three, cause you have to square it is 27 times five. I need a calculator for, um, so you get 135 in the numerator and in the done nomine area of two times to just four times for 16. So when we go to write our answer, I just found the slope under 35 16 x minus your x coordinate, plus your y coordinate. There's 27 8 Now some teachers will make you changes to slope intercept form. I am not one of those, but you can easily if you want to distribute that and combine like terms and use a calculator to get there.

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