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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = (4 x^{2} + 3) (4 x - 5)

\frac{d}{d x} (ln (25))

x \to 0 lim (\frac{( 8 ^{x} - 1 )}{x})

\int \frac{d}{1} (x) d x

\int_{- 3}^{6} 3 + x d x

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