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

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

Simplify

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

= - tan (x)

\int (4 x + 3)^{4} d x

\int - 2 x sin (x) d x

f (x) = 6 x 4 - 3 x, at x = - 2

lo g_{2} (lo g_{2} (x))

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)