In Exercises 5-24, compute the derivative. sec ey =

Answered: In Exercises 5-24, compute the…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.9: Direct Variation

Problem 1WE

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In Exercises 5-24, compute the derivative.

Expert Solution

Solution

Given : $y = \frac{s e c θ}{θ}$

To find: $\frac{d y}{dθ}$

differentiate both sides with respect to $θ$ in the given expression

$\Rightarrow \frac{d y}{d θ} = \frac{d (\frac{s e c θ}{θ})}{d θ}$

= $\frac{θ s e c θ \tan θ - s e c θ}{θ^{2^{}}}$ [ $\frac{d (\frac{f (x)}{g (x)})}{d x} = \frac{g (x) \frac{d (f (x))}{d x} - f (x) \frac{d (g (x))}{d x}}{(g {(x))}^{2}}$ ]

= $\frac{s e c θ (θ \tan θ - 1)}{θ^{2}}$

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In Exercises 5-24, compute the derivative. sec e y =