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

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

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

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

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derivative of

y = 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 )}

\int_{0}^{9} \frac{1}{81 + x ^{2}} d x

\int sec^{5} (t) d t

\frac{\partial ^{2}}{\partial x ^{2}} (x^{2} - e^{y^{2}})

ln ∣ sec (θ) + tan (θ) ∣

\int_{0}^{1} \frac{x ^{4} + 2}{x} d x

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