What is the derivative of log_{4}(sec(x)) ?

The derivative of log_{4}(sec(x)) is (tan(x))/(2ln(2))

What is the first derivative of log_{4}(sec(x)) ?

The first derivative of log_{4}(sec(x)) is (tan(x))/(2ln(2))

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\frac{d}{d x} (lo g_{4} (sec (x)))

\frac{tan ( x )}{2 ln ( 2 )}

Solution steps

\frac{d}{d x} (lo g_{4} (sec (x)))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( sec ( x ) )}{ln ( 4 )})

Take the constant out:

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

= \frac{1}{ln ( 4 )} \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 ( 4 )} \cdot \frac{1}{sec ( x )} sec (x) tan (x)

Simplify

\frac{1}{ln ( 4 )} \cdot \frac{1}{sec ( x )} sec (x) tan (x) : \frac{tan ( x )}{2 ln ( 2 )}

= \frac{tan ( x )}{2 ln ( 2 )}

\frac{d}{d x} (3 x^{2} - \frac{1}{x ^{2}})

16 y^{^{''}} + 8 y^{^{'}} + y = 0

\int_{1}^{\infty} x e^{- 10 x} d x

x \to 0 lim (\frac{x + 1}{5 x})

x^{2} - 2, 7

What is the derivative of log_{4}(sec(x)) ?
The derivative of log_{4}(sec(x)) is (tan(x))/(2ln(2))
What is the first derivative of log_{4}(sec(x)) ?
The first derivative of log_{4}(sec(x)) is (tan(x))/(2ln(2))