Use logarithmic differentiation to find dy/dx. y- + 1(x - 7). (x - 1)(x + 7) x> 7 Step 1 The given function y is positive for all x greater than seven. Hence, the function In y is defined defined in the domain of x. Obtain the natural logarithm of the function y, using the logarithmic properties In ab = In a + In b and In = In a - In b, where a and b are positive. In y = In(x + 1) + + In(x - 7) - -| In(x- 1) - In(x + 7) Step 2 Use the rule for logarithmic differentiation, (In x)= Obtain the derivative, dy dx Step 3 Simplify the expression. Rearrange the terms on the right side.

Use logarithmic differentiation to find dy/dx. y- + 1(x - 7). (x - 1)(x + 7) x> 7 Step 1 The given function y is positive for all x greater than seven. Hence, the function In y is defined defined in the domain of x. Obtain the natural logarithm of the function y, using the logarithmic properties In ab = In a + In b and In = In a - In b, where a and b are positive. In y = In(x + 1) + + In(x - 7) - -| In(x- 1) - In(x + 7) Step 2 Use the rule for logarithmic differentiation, (In x)= Obtain the derivative, dy dx Step 3 Simplify the expression. Rearrange the terms on the right side.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.7: Exponential And Logarithmic Models

Problem 27SE: Prove that bx=exln(b) for positive b1 .

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