Question

Differentiate the function. $F(z)=\frac{A+B z+C z^2}{z^2}$

   Differentiate the function.
$F(z)=\frac{A+B z+C z^2}{z^2}$
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 3, Problem 29 ↓
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Differentiate the function. $F(z)=\frac{A+B z+C z^2}{z^2}$
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Transcript

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00:01 The first thing i would do is manipulate the division, the quotient, because we have a plus b, z, plus c, z squared, all over z squared.
00:16 And for whatever reason, students are good with knowing that if you're adding fractions together, your denominator needs to be the same.
00:29 So if your denominator is the same, we can go this way.
00:31 Well, you can also go backwards where you, i guess, divide each piece in the numerator, a, b, z, and c, z squared.
00:46 And the whole point of doing this is 1 z cancels it with the b, and then both z squareds cancel.
00:53 So if i go back to what f of z is equal to, i would rewrite it as a z to the negative second power because that's how you can move a term into the numerator as you negate the exponent.
01:05 So now this is z to the first.
01:07 So i'm going to rewrite as b, z to the negative first.
01:11 And over here you just have a constant.
01:14 So as a reminder on the power rule for the derivative, you move the exponent in front and you multiply by the coefficient, but then you subtract one from the exponent and think about how negative 2 minus 1...
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