Question

Let $f(x) = \frac{x^7(6x+2)^6}{\sqrt{4x^2 - 11}}$. If we use the method of logarithmic differentiation to find $f'(x)$, we obtain $f'(x)$ in the form $f'(x) = \frac{x^7(6x+2)^6}{\sqrt{4x^2 - 11}} \left( A(x) + \frac{B(x)}{6x+2} + \frac{C(x)}{4x^2 - 11} \right)$, where $A(x)$, $B(x)$ and $C(x)$ are functions of $x$. Find them. Answer: $A(x) = ?$ $B(x) = ?$ and $C(x) = ?$

          Let $f(x) = \frac{x^7(6x+2)^6}{\sqrt{4x^2 - 11}}$.
If we use the method of logarithmic differentiation to find $f'(x)$, we obtain $f'(x)$ in the form
$f'(x) = \frac{x^7(6x+2)^6}{\sqrt{4x^2 - 11}} \left( A(x) + \frac{B(x)}{6x+2} + \frac{C(x)}{4x^2 - 11} \right)$, where $A(x)$, $B(x)$ and $C(x)$ are functions of $x$. Find them.
Answer: $A(x) = ?$
$B(x) = ?$ and
$C(x) = ?$

Let f(x) = (x^7(6x+2)^6)/(√(4x^2 - 11)).
If we use the method of logarithmic differentiation to find f'(x), we obtain f'(x) in the form
f'(x) = (x^7(6x+2)^6)/(√(4x^2 - 11))( A(x) + (B(x))/(6x+2) + (C(x))/(4x^2 - 11)), where A(x), B(x) and C(x) are functions of x. Find them.
Answer: A(x) = ?
B(x) = ? and
C(x) = ?

Added by Kayla L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Bradley Duda

07/10/2023

Step 1

Step 1: Start with the given equation f'(x) = (6x + 2)ª √(4x² - 11) = x^7 (6x + 2)^6 √(4x² - 11). Show more…

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Texts: Let f(x): f'(x) = If we use the method of logarithmic differentiation to find f'(x), we obtain f'(x) in the form 27= (6x + 2)ª ( A(x) √4x² - 11 = x^7 (6x + 2)^6 √4x² - 11 Answer. A(x) = B(x) = - and C(x) = + where A(x), B(x) and C(x) are functions of x. Find them. -0 B(x) = 6x + 2 + C(x) = 4x² - 11 If we use the method of logarithmic differentiation to find f, we obtain f in the form C √4x² - 11 where A, B, and C are functions of x. Find them. Answer A = B = C =