Find the derivative of the function. f(x) = sin-¹(7x) Step 1 Wo rocall that the derivative of the funghi..

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 the function.
Step 1
We recall that the derivative of the function y = sin¯¹(x) is given by the following.
f(x) = sin ¹(7x)
√1-x²
We note that for the given function, f(x) = sin¯¹(7x), we will need to combine the formula above with the chain rule as follows, where u = 7x.
du
1
V1-u² dx
U = 7x
du
dx
dx
(sin¯¹(x)) =
d
dx
So, our first step is to determine
(sin¯¹(u))
du
dx
Transcribed Image Text:Find the derivative of the function. Step 1 We recall that the derivative of the function y = sin¯¹(x) is given by the following. f(x) = sin ¹(7x) √1-x² We note that for the given function, f(x) = sin¯¹(7x), we will need to combine the formula above with the chain rule as follows, where u = 7x. du 1 V1-u² dx U = 7x du dx dx (sin¯¹(x)) = d dx So, our first step is to determine (sin¯¹(u)) du dx
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