What is the derivative of ln(xln(x)) ?

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

What is the first derivative of ln(xln(x)) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = 5^{x} ln (5) + \frac{2}{x ^{2} + 1}

X^{5}

y^{^{''}} + 9 y = x e^{x}

\int_{1200}^{1201} 0.1

\frac{d}{d x} (- 5 ln (cos (x)))

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