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Popular >

derivative of f(x)=ln(5+ln(x))

Solution

derivative of

f (x) = ln (5 + ln (x))

Solution

\frac{1}{x ( 5 + ln ( x ) )}

Solution steps

\frac{d}{d x} (ln (5 + ln (x)))

Apply the chain rule:

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

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

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

= \frac{1}{5 + ln ( x )} \cdot \frac{1}{x}

Simplify

\frac{1}{5 + ln ( x )} \cdot \frac{1}{x} : \frac{1}{x ( 5 + ln ( x ) )}

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

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=ln(5+ln(x)) ?
The derivative of f(x)=ln(5+ln(x)) is 1/(x(5+ln(x)))
What is the first derivative of f(x)=ln(5+ln(x)) ?
The first derivative of f(x)=ln(5+ln(x)) is 1/(x(5+ln(x)))