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

The derivative of 1/(n(1+ln(x))^2) is -2/(nx(1+ln(x))^3)

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

The first derivative of 1/(n(1+ln(x))^2) is -2/(nx(1+ln(x))^3)

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

\frac{1}{n}

(3 x^{2} + 7) (6 x + 3)

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

y = \frac{6 t + 1}{5}

What is the derivative of 1/(n(1+ln(x))^2) ?
The derivative of 1/(n(1+ln(x))^2) is -2/(nx(1+ln(x))^3)
What is the first derivative of 1/(n(1+ln(x))^2) ?
The first derivative of 1/(n(1+ln(x))^2) is -2/(nx(1+ln(x))^3)