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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

3 (sin (2 x) cos (x) - sin^{3} (x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 (sin (2 x) cos (x) + (- sin (x)) sin^{2} (x)) : 3 (sin (2 x) cos (x) - sin^{3} (x))

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

\frac{d}{d x} (\frac{3 x - 2}{2 x + 1})

\frac{d}{d x} (x \cdot x - 3 x)

\frac{d}{d t} (t, t^{2}, t^{3})

x \to 3 - lim (\frac{2 - x}{x - 3})

f (x) = - 2 x^{3}, (- 2, 16)

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