What is the derivative of log_{4}(cos(2x)) ?

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

What is the first derivative of log_{4}(cos(2x)) ?

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

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\frac{d}{d x} (lo g_{4} (cos (2 x)))

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

Solution steps

\frac{d}{d x} (lo g_{4} (cos (2 x)))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( cos ( 2 x ) )}{ln ( 4 )})

Take the constant out:

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

= \frac{1}{ln ( 4 )} \frac{d}{d x} (ln (cos (2 x)))

Apply the chain rule:

\frac{1}{cos ( 2 x )} \frac{d}{d x} (cos (2 x))

= \frac{1}{cos ( 2 x )} \frac{d}{d x} (cos (2 x))

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= \frac{1}{ln ( 4 )} \cdot \frac{1}{cos ( 2 x )} (- sin (2 x) \cdot 2)

Simplify

\frac{1}{ln ( 4 )} \cdot \frac{1}{cos ( 2 x )} (- sin (2 x) \cdot 2) : - \frac{tan ( 2 x )}{ln ( 2 )}

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

\frac{d}{d x} (- \frac{3}{x ^{2}} + 4 e^{2 x})

\int r^{2} + z^{2} d z

\frac{d}{d t} (2 sin (t))

f (x) = \frac{x ^{2}}{3}

\frac{\partial}{\partial y} (2 x + 3 y - 7)

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