derivative of ln(((2x+1^2)/((x-1))))

해법

\frac{d}{d x} (ln (\frac{( 2 x + 1 ) ^{2}}{( x - 1 )}))

\frac{2 x - 5}{( 2 x + 1 ) ( x - 1 )}

솔루션 단계

\frac{d}{d x} (ln (\frac{( 2 x + 1 ) ^{2}}{( x - 1 )}))

체인 규칙 적용:

\frac{1}{\frac{( 2 x + 1 ) ^{2}}{x - 1}} \frac{d}{d x} (\frac{( 2 x + 1 ) ^{2}}{x - 1})

= \frac{1}{\frac{( 2 x + 1 ) ^{2}}{x - 1}} \frac{d}{d x} (\frac{( 2 x + 1 ) ^{2}}{x - 1})

\frac{d}{d x} (\frac{( 2 x + 1 ) ^{2}}{x - 1}) = \frac{4 x ^{2} - 8 x - 5}{( x - 1 ) ^{2}}

= \frac{1}{\frac{( 2 x + 1 ) ^{2}}{x - 1}} \cdot \frac{4 x ^{2} - 8 x - 5}{( x - 1 ) ^{2}}

\frac{1}{\frac{( 2 x + 1 ) ^{2}}{x - 1}} \cdot \frac{4 x ^{2} - 8 x - 5}{( x - 1 ) ^{2}}

간소화하다 :

\frac{2 x - 5}{( 2 x + 1 ) ( x - 1 )}

= \frac{2 x - 5}{( 2 x + 1 ) ( x - 1 )}