What is the derivative of-(ln(2)/(x(x+ln(2)))) ?

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

What is the first derivative of-(ln(2)/(x(x+ln(2)))) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d x}{d y} = - x^{2} + 7 x - 8

\int \frac{x ^{4} - 2 x ^{2} + 3}{x ^{2}} d x

\int x + 4 y d x

n = 1 \sum \infty \frac{n ^{n}}{n !}

4 \frac{d y}{d x} + 28 y = 7

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