What is the derivative of ln(12cos^2(x)) ?

The derivative of ln(12cos^2(x)) is -2tan(x)

What is the first derivative of ln(12cos^2(x)) ?

The first derivative of ln(12cos^2(x)) is -2tan(x)

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\frac{d}{d x} (ln (12 cos^{2} (x)))

- 2 tan (x)

Solution steps

\frac{d}{d x} (ln (12 cos^{2} (x)))

Apply the chain rule:

\frac{1}{12 cos ^{2} ( x )} \frac{d}{d x} (12 cos^{2} (x))

= \frac{1}{12 cos ^{2} ( x )} \frac{d}{d x} (12 cos^{2} (x))

\frac{d}{d x} (12 cos^{2} (x)) = - 24 cos (x) sin (x)

= \frac{1}{12 cos ^{2} ( x )} (- 24 cos (x) sin (x))

Simplify

\frac{1}{12 cos ^{2} ( x )} (- 24 cos (x) sin (x)) : - 2 tan (x)

= - 2 tan (x)

x \to 0 lim (x lo g_{e} (x))

\frac{d}{d x} ((1 + \frac{2}{x})^{x})

\frac{d}{d x} (\frac{e ^{3 x}}{e ^{3 x} + 2})

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

\int (\frac{1}{x ^{3}}) d x

What is the derivative of ln(12cos^2(x)) ?
The derivative of ln(12cos^2(x)) is -2tan(x)
What is the first derivative of ln(12cos^2(x)) ?
The first derivative of ln(12cos^2(x)) is -2tan(x)