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Find the derivative. 9 t z(t) = 9+t dz dt

Find the derivative. 9 t z(t) = 9+t dz dt

Advanced Engineering Mathematics
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 \(v = 9 + t\).
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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