What is the derivative of ln(ln(9x)+ln(ln(9))) ?

The derivative of ln(ln(9x)+ln(ln(9))) is 1/(xln(9x))

What is the first derivative of ln(ln(9x)+ln(ln(9))) ?

The first derivative of ln(ln(9x)+ln(ln(9))) is 1/(xln(9x))

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\frac{d}{d x} (ln (ln (9 x)) + ln (ln (9)))

\frac{1}{x ln ( 9 x )}

Solution steps

\frac{d}{d x} (ln (ln (9 x)) + ln (ln (9)))

Simplify

ln (ln (9 x)) + ln (ln (9)) : ln (2 ln (3) ln (9 x))

= \frac{d}{d x} (ln (2 ln (3) ln (9 x)))

Apply the chain rule:

\frac{1}{2 ln ( 3 ) ln ( 9 x )} \frac{d}{d x} (2 ln (3) ln (9 x))

= \frac{1}{2 ln ( 3 ) ln ( 9 x )} \frac{d}{d x} (2 ln (3) ln (9 x))

\frac{d}{d x} (2 ln (3) ln (9 x)) = \frac{2 ln ( 3 )}{x}

= \frac{1}{2 ln ( 3 ) ln ( 9 x )} \cdot \frac{2 ln ( 3 )}{x}

Simplify

\frac{1}{2 ln ( 3 ) ln ( 9 x )} \cdot \frac{2 ln ( 3 )}{x} : \frac{1}{x ln ( 9 x )}

= \frac{1}{x ln ( 9 x )}

\frac{d}{d y} (e^{3 y})

\int \frac{x ^{2}}{e ^{3 x}} d x

x \to 0 lim (5 x + 3 - 2 x^{2})

x = 7 y^{2}, x = 4 + 6 y^{2}

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

What is the derivative of ln(ln(9x)+ln(ln(9))) ?
The derivative of ln(ln(9x)+ln(ln(9))) is 1/(xln(9x))
What is the first derivative of ln(ln(9x)+ln(ln(9))) ?
The first derivative of ln(ln(9x)+ln(ln(9))) is 1/(xln(9x))