e think of In(-3x + 7) as In(u), then u is a differentiable function of x and u = tionally, if we think of In(x + 7) as In(v), then v is a differentiable function of x and v all that the derivative of a sum is the sum of the derivatives. Apply the generalized rule to find the derivative of In(u) + In(v). D [In(-3x + 7) + In(x + 7)] = = dx [In(u) + In(v)] dx dx [In(u)] = - 1. du dx + [n[ ]] dv dx
e think of In(-3x + 7) as In(u), then u is a differentiable function of x and u = tionally, if we think of In(x + 7) as In(v), then v is a differentiable function of x and v all that the derivative of a sum is the sum of the derivatives. Apply the generalized rule to find the derivative of In(u) + In(v). D [In(-3x + 7) + In(x + 7)] = = dx [In(u) + In(v)] dx dx [In(u)] = - 1. du dx + [n[ ]] dv dx
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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Question
![Step 2
Since h(x) = In(−3x + 7) + In(x + 7), we can proceed to find the derivative of h.
If we think of In(−3x + 7) as In(u), then u is a differentiable function of x and u =
Additionally, if we think of In(x + 7) as In(v), then v is a differentiable function of x and v =
Recall that the derivative of a sum is the sum of the derivatives. Apply the generalized rule to find the derivative of In(u) + In(v).
h'(x)
−[In(−3x + 7) + In(x + 7)]
=
=
=
dx
dx
[In(u) + In(v)]
d_[In(u)] +
dx
1 du
dx
H|3
din
In
dx
dv
dx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd48171ba-d1cc-47b1-bf9c-8041143384f0%2F42509cc7-1c21-4b78-af88-172800a8210b%2Fm3kzaev_processed.png&w=3840&q=75)
Transcribed Image Text:Step 2
Since h(x) = In(−3x + 7) + In(x + 7), we can proceed to find the derivative of h.
If we think of In(−3x + 7) as In(u), then u is a differentiable function of x and u =
Additionally, if we think of In(x + 7) as In(v), then v is a differentiable function of x and v =
Recall that the derivative of a sum is the sum of the derivatives. Apply the generalized rule to find the derivative of In(u) + In(v).
h'(x)
−[In(−3x + 7) + In(x + 7)]
=
=
=
dx
dx
[In(u) + In(v)]
d_[In(u)] +
dx
1 du
dx
H|3
din
In
dx
dv
dx
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