What is the derivative of 1/4 ln(cos(4x)) ?

The derivative of 1/4 ln(cos(4x)) is -tan(4x)

What is the first derivative of 1/4 ln(cos(4x)) ?

The first derivative of 1/4 ln(cos(4x)) is -tan(4x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{1}{4} ln (cos (4 x)))

- tan (4 x)

Solution steps

\frac{d}{d x} (\frac{1}{4} ln (cos (4 x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{4} \frac{d}{d x} (ln (cos (4 x)))

Apply the chain rule:

\frac{1}{cos ( 4 x )} \frac{d}{d x} (cos (4 x))

= \frac{1}{cos ( 4 x )} \frac{d}{d x} (cos (4 x))

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

= \frac{1}{4} \cdot \frac{1}{cos ( 4 x )} (- sin (4 x) \cdot 4)

Simplify

\frac{1}{4} \cdot \frac{1}{cos ( 4 x )} (- sin (4 x) \cdot 4) : - tan (4 x)

= - tan (4 x)

\int \frac{1}{1 + e ^{x}} d x

- x^{2} + 10 x - 16, 2 x - 4

\int \frac{1}{x ^{\frac{7}{2}}} d x

\frac{d}{d x} ((f (x) (4 x))^{2} + 5)

6 x + y^{2} = 16, x = y

What is the derivative of 1/4 ln(cos(4x)) ?
The derivative of 1/4 ln(cos(4x)) is -tan(4x)
What is the first derivative of 1/4 ln(cos(4x)) ?
The first derivative of 1/4 ln(cos(4x)) is -tan(4x)