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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (1) = 0

= - \frac{1}{x ln ^{2} ( x )} - (- \frac{1}{x ^{2}}) - 0

Simplify

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

3 t^{2} + 1

y = \frac{( 5 x + 9 )}{( x - 1 )}

y = x^{3} + x^{2} + x + 1

\frac{1}{g}

(x - 2)^{3}

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