What is the derivative of ln(1+cos(x)) ?

The derivative of ln(1+cos(x)) is -(sin(x))/(1+cos(x))

What is the first derivative of ln(1+cos(x)) ?

The first derivative of ln(1+cos(x)) is -(sin(x))/(1+cos(x))

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derivative of

ln (1 + cos (x))

- \frac{sin ( x )}{1 + cos ( x )}

Solution steps

\frac{d}{d x} (ln (1 + cos (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (1 + cos (x)) = - sin (x)

= \frac{1}{1 + cos ( x )} (- sin (x))

Simplify

\frac{1}{1 + cos ( x )} (- sin (x)) : - \frac{sin ( x )}{1 + cos ( x )}

= - \frac{sin ( x )}{1 + cos ( x )}

\frac{d}{d a} (1 + 6 cos^{2} (a) + cos^{4} (a))

f (x) = x^{6} - x^{4} - 2

x (x^{2} + 4)^{0.5}

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

\frac{d}{d t} (12 + 6 t)

What is the derivative of ln(1+cos(x)) ?
The derivative of ln(1+cos(x)) is -(sin(x))/(1+cos(x))
What is the first derivative of ln(1+cos(x)) ?
The first derivative of ln(1+cos(x)) is -(sin(x))/(1+cos(x))