What is the derivative of log_{e}(sec(1/(5x))) ?

The derivative of log_{e}(sec(1/(5x))) is -(tan(1/(5x)))/(5x^2)

What is the first derivative of log_{e}(sec(1/(5x))) ?

The first derivative of log_{e}(sec(1/(5x))) is -(tan(1/(5x)))/(5x^2)

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derivative of

lo g_{e} (sec (\frac{1}{5 x}))

- \frac{tan ( \frac{1}{5 x} )}{5 x ^{2}}

Solution steps

\frac{d}{d x} (lo g_{e} (sec (\frac{1}{5 x})))

Simplify

lo g_{e} (sec (\frac{1}{5 x})) : ln (sec (\frac{1}{5 x}))

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

Apply the chain rule:

\frac{1}{sec ( \frac{1}{5 x} )} \frac{d}{d x} (sec (\frac{1}{5 x}))

= \frac{1}{sec ( \frac{1}{5 x} )} \frac{d}{d x} (sec (\frac{1}{5 x}))

\frac{d}{d x} (sec (\frac{1}{5 x})) = - \frac{sec ( \frac{1}{5 x} ) tan ( \frac{1}{5 x} )}{5 x ^{2}}

= \frac{1}{sec ( \frac{1}{5 x} )} (- \frac{sec ( \frac{1}{5 x} ) tan ( \frac{1}{5 x} )}{5 x ^{2}})

Simplify

\frac{1}{sec ( \frac{1}{5 x} )} (- \frac{sec ( \frac{1}{5 x} ) tan ( \frac{1}{5 x} )}{5 x ^{2}}) : - \frac{tan ( \frac{1}{5 x} )}{5 x ^{2}}

= - \frac{tan ( \frac{1}{5 x} )}{5 x ^{2}}

\frac{5}{s ^{2}}

\int e^{2 t} cos (e^{t}) d t

x \to + 3 + lim (\frac{x + 9}{x - 3})

\frac{d}{d x} (3 tan^{2} (x))

\frac{r}{r ^{2} + 9}

What is the derivative of log_{e}(sec(1/(5x))) ?
The derivative of log_{e}(sec(1/(5x))) is -(tan(1/(5x)))/(5x^2)
What is the first derivative of log_{e}(sec(1/(5x))) ?
The first derivative of log_{e}(sec(1/(5x))) is -(tan(1/(5x)))/(5x^2)