en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 6ln(cos(x))

Solution

\frac{d}{d x} (6 ln (cos (x)))

Solution

- 6 tan (x)

Solution steps

\frac{d}{d x} (6 ln (cos (x)))

Take the constant out:

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

= 6 \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)) = - sin (x)

= 6 \cdot \frac{1}{cos ( x )} (- sin (x))

Simplify

6 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 6 tan (x)

= - 6 tan (x)

Popular Examples

(\partial)/(\partial x)(e^{xy}sin(y))

\frac{\partial}{\partial x} (e^{x y} sin (y))

limit as x approaches 0 of 9x^2-2x+5

x \to 0 lim (9 x^{2} - 2 x + 5)

(\partial)/(\partial b)(10^{-2b})

\frac{\partial}{\partial b} (1 0^{- 2 b})

integral of (x^2)/(x^2+x-6)

\int \frac{x ^{2}}{x ^{2} + x - 6} d x

limit as x approaches 0 of (sin(-x))/x

x \to 0 lim (\frac{sin ( - x )}{x})

Frequently Asked Questions (FAQ)

What is the derivative of 6ln(cos(x)) ?
The derivative of 6ln(cos(x)) is -6tan(x)
What is the first derivative of 6ln(cos(x)) ?
The first derivative of 6ln(cos(x)) is -6tan(x)