What is the derivative of 3sin^2(xcos(2x)) ?

The derivative of 3sin^2(xcos(2x)) is 3((sin(4x))/2-4sin^3(x)cos(x))

What is the first derivative of 3sin^2(xcos(2x)) ?

The first derivative of 3sin^2(xcos(2x)) is 3((sin(4x))/2-4sin^3(x)cos(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (3 sin^{2} (x) cos (2 x))

3 (\frac{sin ( 4 x )}{2} - 4 sin^{3} (x) cos (x))

Solution steps

\frac{d}{d x} (3 sin^{2} (x) cos (2 x))

Take the constant out:

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

= 3 \frac{d}{d x} (sin^{2} (x) cos (2 x))

Apply the Product Rule:

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

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

= 3 (\frac{d}{d x} (sin^{2} (x)) cos (2 x) + \frac{d}{d x} (cos (2 x)) sin^{2} (x))

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

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

= 3 (sin (2 x) cos (2 x) + (- sin (2 x) \cdot 2) sin^{2} (x))

Simplify

3 (sin (2 x) cos (2 x) + (- sin (2 x) \cdot 2) sin^{2} (x)) : 3 (\frac{sin ( 4 x )}{2} - 4 sin^{3} (x) cos (x))

= 3 (\frac{sin ( 4 x )}{2} - 4 sin^{3} (x) cos (x))

What is the derivative of 3sin^2(xcos(2x)) ?
The derivative of 3sin^2(xcos(2x)) is 3((sin(4x))/2-4sin^3(x)cos(x))
What is the first derivative of 3sin^2(xcos(2x)) ?
The first derivative of 3sin^2(xcos(2x)) is 3((sin(4x))/2-4sin^3(x)cos(x))