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

The derivative of ln(cos^2(x)) is -2tan(x)

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

The first derivative of ln(cos^2(x)) is -2tan(x)

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\frac{d}{d x} (ln (cos^{2} (x)))

- 2 tan (x)

Solution steps

\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)

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

Simplify

\frac{1}{cos ^{2} ( x )} (- sin (2 x)) : - 2 tan (x)

= - 2 tan (x)

What is the derivative of ln(cos^2(x)) ?
The derivative of ln(cos^2(x)) is -2tan(x)
What is the first derivative of ln(cos^2(x)) ?
The first derivative of ln(cos^2(x)) is -2tan(x)