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

The derivative of ln(cos(x)) is -tan(x)

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

The first derivative of ln(cos(x)) is -tan(x)

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derivative of

ln (cos (x))

- tan (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - tan (x)

d y = (x - 2 y (cot (2 x))) d x

\frac{d}{d x} (lo g_{10} (1 + x))

\frac{d}{d x} (tan (x) + 3 co tan (x))

\int (x^{\frac{3}{2}}) d x

y^{^{''}} + 6 y^{^{'}} + 18 y = - 9 e^{- 3 t}

What is the derivative of ln(cos(x)) ?
The derivative of ln(cos(x)) is -tan(x)
What is the first derivative of ln(cos(x)) ?
The first derivative of ln(cos(x)) is -tan(x)