What is the derivative of ln(4/(xsqrt(x+1))) ?

The derivative of ln(4/(xsqrt(x+1))) is -(3x+2)/(2x(x+1))

What is the first derivative of ln(4/(xsqrt(x+1))) ?

The first derivative of ln(4/(xsqrt(x+1))) is -(3x+2)/(2x(x+1))

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\frac{d}{d x} (ln (\frac{4}{x x + 1}))

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

Solution steps

\frac{d}{d x} (ln (\frac{4}{x x + 1}))

Apply the chain rule:

\frac{1}{\frac{4}{x x + 1}} \frac{d}{d x} (\frac{4}{x x + 1})

= \frac{1}{\frac{4}{x x + 1}} \frac{d}{d x} (\frac{4}{x x + 1})

\frac{d}{d x} (\frac{4}{x x + 1}) = - \frac{2 ( 3 x + 2 )}{x ^{2} ( x + 1 ) x + 1}

= \frac{1}{\frac{4}{x x + 1}} (- \frac{2 ( 3 x + 2 )}{x ^{2} ( x + 1 ) x + 1})

Simplify

\frac{1}{\frac{4}{x x + 1}} (- \frac{2 ( 3 x + 2 )}{x ^{2} ( x + 1 ) x + 1}) : - \frac{3 x + 2}{2 x ( x + 1 )}

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

\frac{\partial}{\partial x} (- 2 x y)

\frac{d}{d x} ((x^{3} - 4 x + 1) e^{x})

x \to 0 lim (\frac{5}{tan ( 3 x )})

8 \frac{d y}{d x} + 7 e^{x + y} = 0

y^{^{'}} = t y

What is the derivative of ln(4/(xsqrt(x+1))) ?
The derivative of ln(4/(xsqrt(x+1))) is -(3x+2)/(2x(x+1))
What is the first derivative of ln(4/(xsqrt(x+1))) ?
The first derivative of ln(4/(xsqrt(x+1))) is -(3x+2)/(2x(x+1))