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

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

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

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

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\frac{d}{d x} (\frac{x}{x - 1} - \frac{1}{ln ( x )})

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

Solution steps

\frac{d}{d x} (\frac{x}{x - 1} - \frac{1}{ln ( x )})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x}{x - 1}) - \frac{d}{d x} (\frac{1}{ln ( x )})

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

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

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

Simplify

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

y = x^{2} + 3, (- 5, 28)

f (x) = x^{2} + x

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

\frac{d}{d x} (sec (x) + tan (x))

\frac{13}{x}

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