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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{\frac{x ^{2}}{x + 1}} \cdot \frac{x ^{2} + 2 x}{( x + 1 ) ^{2}} : \frac{x + 2}{x ( x + 1 )}

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

f (x) = (3 a + 1)^{2}

x \to + 6 lim (36 - x^{2})

x \to + 1 lim (e^{x^{2} - x})

y^{^{'}} + x^{2} sin (y) = 0

f (x) = x^{3} - 5 x^{2}, at x = 0

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