What is the derivative of ln(4-2cos(x)) ?

The derivative of ln(4-2cos(x)) is (sin(x))/(2-cos(x))

What is the first derivative of ln(4-2cos(x)) ?

The first derivative of ln(4-2cos(x)) is (sin(x))/(2-cos(x))

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derivative of

ln (4 - 2 cos (x))

\frac{sin ( x )}{2 - cos ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of ln(4-2cos(x)) ?
The derivative of ln(4-2cos(x)) is (sin(x))/(2-cos(x))
What is the first derivative of ln(4-2cos(x)) ?
The first derivative of ln(4-2cos(x)) is (sin(x))/(2-cos(x))