What is the derivative of ln(((2x+1^2)/((x-1)))) ?

The derivative of ln(((2x+1^2)/((x-1)))) is (2x-5)/((2x+1)(x-1))

What is the first derivative of ln(((2x+1^2)/((x-1)))) ?

The first derivative of ln(((2x+1^2)/((x-1)))) is (2x-5)/((2x+1)(x-1))

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

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

Solution steps

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

Apply the chain rule:

\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}}

Simplify

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

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

\frac{( 2 s + 1 )}{s ^{2} + 10 + 25}

tan (3 x), 2 sin (3 x), - \frac{π}{9}, \frac{π}{9}

\int x^{2} 7 + x d x

\int t^{2} 7 t - 5 d t

x \to 0 + lim (ln ∣ x ∣)

What is the derivative of ln(((2x+1^2)/((x-1)))) ?
The derivative of ln(((2x+1^2)/((x-1)))) is (2x-5)/((2x+1)(x-1))
What is the first derivative of ln(((2x+1^2)/((x-1)))) ?
The first derivative of ln(((2x+1^2)/((x-1)))) is (2x-5)/((2x+1)(x-1))