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

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

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

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

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

\frac{x + 2}{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}{2 x ^{2} ( x + 1 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x ^{2}}{x + 1}} \cdot \frac{x ^{2} + 2 x}{2 x ^{2} ( x + 1 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{\frac{x ^{2}}{x + 1}} \cdot \frac{x ^{2} + 2 x}{2 x ^{2} ( x + 1 ) ^{\frac{3}{2}}} : \frac{x + 2}{2 x ( x + 1 )}

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

\int \frac{( cos ( x ) )}{( ( sin ^{2} ( x ) ) ^{\frac{1}{3}} )} d x

\frac{d}{d t} (t^{2} + 4 t)

y^{^{'}} + 10 y = 1

x \to 0 lim (2 + (\frac{3}{x}))

\frac{\partial}{\partial y} (x y + \frac{1}{x} + \frac{1}{y})

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