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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
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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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
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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