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Find the derivative of y with respect to t: y = sec -¹ (9t5 + 8). dy dt

Find the derivative of y with respect to t: y = sec -¹ (9t5 + 8). dy dt

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the derivative of \( y \) with respect to \( t \): \( y = \sec^{-1}(9t^5 + 8) \). \[ \frac{dy}{dt} = \boxed{} \]
Transcribed Image Text:Find the derivative of \( y \) with respect to \( t \): \( y = \sec^{-1}(9t^5 + 8) \). \[ \frac{dy}{dt} = \boxed{} \]
Expert Solution
Step 1

As we know that:

The Power law:

ddxxn=nxn-1

The Chain rule:

fgx'=f'gx·g'x

And use the derivative of sec-1x.

ddxsec-1x=1xx2-1, x>1

 

Given:

y=sec-19t5+8

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