What is the -derivative of cos(3x) ?

The -derivative of cos(3x) is -x derivative of cos(3x)-3xsin(3x)-cos(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

Find the Derivative - d/dx cos(3x)

\int - \frac{d}{d x} (cos (3 x)) d x

- x \frac{d}{d x} (cos (3 x)) - 3 x sin (3 x) - cos (3 x) + C

Solution steps

\int - \frac{d}{d x} (cos (3 x)) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{d}{d x} (cos (3 x)) d x

Apply Integration By Parts

: x \frac{d}{d x} (cos (3 x)) - \int - 9 x cos (3 x) d x

= - (x \frac{d}{d x} (cos (3 x)) - \int - 9 x cos (3 x) d x)

\int - 9 x cos (3 x) d x = - 3 x sin (3 x) - cos (3 x)

= - (x \frac{d}{d x} (cos (3 x)) - (- 3 x sin (3 x) - cos (3 x)))

Simplify

= - x \frac{d}{d x} (cos (3 x)) - 3 x sin (3 x) - cos (3 x)

Add a constant to the solution

= - x \frac{d}{d x} (cos (3 x)) - 3 x sin (3 x) - cos (3 x) + C

f (x) = arctan (x)

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

- \frac{d}{d x} (x y)

x, y = 0, x = 2, y = x

csc (x) cot (x)

What is the -derivative of cos(3x) ?
The -derivative of cos(3x) is -x derivative of cos(3x)-3xsin(3x)-cos(3x)+C