Differentiate the function.
$$g ( x ) = \frac { \ln x } { x + 4 }$$
A) $\frac { 1 } { x ( x + 4 ) }$
B) $\frac { x ( 1 - \ln x ) + 4 } { x ( x + 4 ) ^ { 2 } }$
C) $\frac { x ( 4 - \ln x ) + 1 } { x ( x + 4 ) ^ { 2 } }$
D) $- \frac { 1 } { x ( x + 4 ) ^ { 2 } }$

Question

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The derivative of $g(x)$ is:$$g'(x) = \frac{(x+4)\frac{d}{dx}[\ln x] - \ln x \frac{d}{dx}[x+4]}{(x+4)^2}$$$$g'(x) = \frac{(x+4)\frac{1}{x} - \ln x (1)}{(x+4)^2}$$$$g'(x) = \frac{x+4-\ln x}{x(x+4)^2}$$$$g'(x) = \frac{x(1-\ln x)+4}{x(x+4)^2}$$

Differentiate the Function g(x)=ln⁡xx+4g ( x ) = \frac { \ln x } { x + 4 }g(x)=x+4lnx​

Differentiate the Function $g ( x ) = \frac { \ln x } { x + 4 }$