What is the derivative of log_{3}(sec(x)) ?

The derivative of log_{3}(sec(x)) is (tan(x))/(ln(3))

What is the first derivative of log_{3}(sec(x)) ?

The first derivative of log_{3}(sec(x)) is (tan(x))/(ln(3))

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\frac{d}{d x} (lo g_{3} (sec (x)))

\frac{tan ( x )}{ln ( 3 )}

Solution steps

\frac{d}{d x} (lo g_{3} (sec (x)))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( sec ( x ) )}{ln ( 3 )})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= \frac{1}{ln ( 3 )} \cdot \frac{1}{sec ( x )} sec (x) tan (x)

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{sec ( x )} sec (x) tan (x) : \frac{tan ( x )}{ln ( 3 )}

= \frac{tan ( x )}{ln ( 3 )}

f (x) = \frac{x}{1 + x ^{2}}, (0, 0)

\frac{d}{d x} (\frac{3 - sec ( x )}{tan ( x )})

\frac{\partial}{\partial y} (ln (x - 2 y + 3 z))

\int_{- e^{2}}^{- e} \frac{3}{x} d x

\int \frac{1}{x ^{2} + 4 x + 3} d x

What is the derivative of log_{3}(sec(x)) ?
The derivative of log_{3}(sec(x)) is (tan(x))/(ln(3))
What is the first derivative of log_{3}(sec(x)) ?
The first derivative of log_{3}(sec(x)) is (tan(x))/(ln(3))