# Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 29

$$- \tan x + \frac{{3x}}{{4 - 3{x^2}}}$$

#### Work Step by Step

\eqalign{ & \frac{d}{{dx}}\left[ {\ln \frac{{\cos x}}{{\sqrt {4 - 3{x^2}} }}} \right] \cr & {\text{radical property}} \cr & \frac{d}{{dx}}\left[ {\ln \frac{{\cos x}}{{{{\left( {4 - 3{x^2}} \right)}^{1/2}}}}} \right] \cr & {\text{logarithm of a quotient}} \cr & = \frac{d}{{dx}}\left[ {\ln \left( {\cos x} \right) - \ln {{\left( {4 - 3{x^2}} \right)}^{1/2}}} \right] \cr & {\text{power rule for logarithms}} \cr & = \frac{d}{{dx}}\left[ {\ln \left( {\cos x} \right) - \frac{1}{2}\ln \left( {4 - 3{x^2}} \right)} \right] \cr & {\text{differentiate}} \cr & = \frac{{ - \sin x}}{{\cos x}} - \frac{1}{2}\left( {\frac{{ - 6x}}{{4 - 3{x^2}}}} \right) \cr & {\text{simplify}} \cr & = - \tan x + \frac{{3x}}{{4 - 3{x^2}}} \cr}

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