Find the derivative. 9 t z(t) = 9+t dz dt
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The task is to find the derivative of the function given by:
\[ z(t) = \frac{9 - t}{9 + t} \]
The derivative is represented as:
\[ \frac{dz}{dt} = \]
To calculate the derivative, you can apply the quotient rule, which states that if you have a function \(\frac{u}{v}\), the derivative is given by:
\[ \frac{d}{dt}\left(\frac{u}{v}\right) = \frac{v \frac{du}{dt} - u \frac{dv}{dt}}{v^2} \]
Here, \(u = 9 - t\) and \(v = 9 + t\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28b0c599-bbea-4dfa-aec4-e0091988eaa4%2F0e2e814b-b8b3-4351-9af3-911b6629eb76%2F4tv0da9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to find the derivative of the function given by:
\[ z(t) = \frac{9 - t}{9 + t} \]
The derivative is represented as:
\[ \frac{dz}{dt} = \]
To calculate the derivative, you can apply the quotient rule, which states that if you have a function \(\frac{u}{v}\), the derivative is given by:
\[ \frac{d}{dt}\left(\frac{u}{v}\right) = \frac{v \frac{du}{dt} - u \frac{dv}{dt}}{v^2} \]
Here, \(u = 9 - t\) and \(v = 9 + t\).
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