What is the derivative of ln(cos(9x)) ?

The derivative of ln(cos(9x)) is -9tan(9x)

What is the first derivative of ln(cos(9x)) ?

The first derivative of ln(cos(9x)) is -9tan(9x)

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\frac{d}{d x} (ln (cos (9 x)))

- 9 tan (9 x)

Solution steps

\frac{d}{d x} (ln (cos (9 x)))

Apply the chain rule:

\frac{1}{cos ( 9 x )} \frac{d}{d x} (cos (9 x))

= \frac{1}{cos ( 9 x )} \frac{d}{d x} (cos (9 x))

\frac{d}{d x} (cos (9 x)) = - sin (9 x) \cdot 9

= \frac{1}{cos ( 9 x )} (- sin (9 x) \cdot 9)

Simplify

\frac{1}{cos ( 9 x )} (- sin (9 x) \cdot 9) : - 9 tan (9 x)

= - 9 tan (9 x)

x \to 5 lim (\frac{sin ( 5 π )}{3})

n = 1 \sum \infty \frac{40}{4 ^{n}}

\frac{\partial}{\partial x} (x^{2} + 8 y^{2} + 9 z^{2} - 7)

\frac{d}{d x} (f (x) (5 x^{2} + 3))

\int x^{3} x^{4} + 10 d x

What is the derivative of ln(cos(9x)) ?
The derivative of ln(cos(9x)) is -9tan(9x)
What is the first derivative of ln(cos(9x)) ?
The first derivative of ln(cos(9x)) is -9tan(9x)