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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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

x^{2} 1, 0, 1

\frac{4 s ^{3}}{( s + 5 ) ^{9}}

x \to 2 lim (5 x - 6)

\frac{\partial}{\partial x} (x z + yz + x y)

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