What is the derivative of xsin(9x) ?

The derivative of xsin(9x) is sin(9x)+9xcos(9x)

What is the first derivative of xsin(9x) ?

The first derivative of xsin(9x) is sin(9x)+9xcos(9x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x sin (9 x))

sin (9 x) + 9 x cos (9 x)

Solution steps

\frac{d}{d x} (x sin (9 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (9 x)

= \frac{d x}{d x} sin (9 x) + \frac{d}{d x} (sin (9 x)) x

\frac{d x}{d x} = 1

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

= 1 \cdot sin (9 x) + cos (9 x) \cdot 9 x

Simplify

= sin (9 x) + 9 x cos (9 x)

What is the derivative of xsin(9x) ?
The derivative of xsin(9x) is sin(9x)+9xcos(9x)
What is the first derivative of xsin(9x) ?
The first derivative of xsin(9x) is sin(9x)+9xcos(9x)