What is the derivative of 2x^2cos(2x) ?

The derivative of 2x^2cos(2x) is 2(2xcos(2x)-2x^2sin(2x))

What is the first derivative of 2x^2cos(2x) ?

The first derivative of 2x^2cos(2x) is 2(2xcos(2x)-2x^2sin(2x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (2 x^{2} cos (2 x))

2 (2 x cos (2 x) - 2 x^{2} sin (2 x))

Solution steps

\frac{d}{d x} (2 x^{2} cos (2 x))

Take the constant out:

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

= 2 \frac{d}{d x} (x^{2} cos (2 x))

Apply the Product Rule:

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

f = x^{2}, g = cos (2 x)

= 2 (\frac{d}{d x} (x^{2}) cos (2 x) + \frac{d}{d x} (cos (2 x)) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= 2 (2 x cos (2 x) + (- sin (2 x) \cdot 2) x^{2})

Simplify

= 2 (2 x cos (2 x) - 2 x^{2} sin (2 x))

What is the derivative of 2x^2cos(2x) ?
The derivative of 2x^2cos(2x) is 2(2xcos(2x)-2x^2sin(2x))
What is the first derivative of 2x^2cos(2x) ?
The first derivative of 2x^2cos(2x) is 2(2xcos(2x)-2x^2sin(2x))