What is the derivative of 1/9 ln(-ln(x)+5) ?

The derivative of 1/9 ln(-ln(x)+5) is 1/(9xln(x))

What is the first derivative of 1/9 ln(-ln(x)+5) ?

The first derivative of 1/9 ln(-ln(x)+5) is 1/(9xln(x))

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\frac{d}{d x} (\frac{1}{9} ln (- ln (x)) + 5)

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

Solution steps

\frac{d}{d x} (\frac{1}{9} ln (- ln (x)) + 5)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{9} ln (- ln (x))) + \frac{d}{d x} (5)

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

\frac{d}{d x} (5) = 0

= \frac{1}{9 x ln ( x )} + 0

Simplify

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

What is the derivative of 1/9 ln(-ln(x)+5) ?
The derivative of 1/9 ln(-ln(x)+5) is 1/(9xln(x))
What is the first derivative of 1/9 ln(-ln(x)+5) ?
The first derivative of 1/9 ln(-ln(x)+5) is 1/(9xln(x))