en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of 4sin^3(2x)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

= 24 sin^{2} (2 x) cos (2 x)

Graph

Popular Examples

integral of 1/((w^2+5)^{3/2)}

\int \frac{1}{( w ^{2} + 5 ) ^{\frac{3}{2}}} d w

derivative of (x^2ln(x)^4)

\frac{d}{d x} ((x^{2} ln (x))^{4})

derivative of y= 1/3 cos((6pix-1)/2)

d er i v a t i v e y = \frac{1}{3} cos (\frac{6 π x - 1}{2})

integral of-e^x-7/(cos^2(x))

\int - e^{x} - \frac{7}{cos ^{2} ( x )} d x

integral of 3/2 e^{3/2 x}

\int \frac{3}{2} e^{\frac{3}{2} x} d x

Frequently Asked Questions (FAQ)

What is the derivative of 4sin^3(2x) ?
The derivative of 4sin^3(2x) is 24sin^2(2x)cos(2x)
What is the first derivative of 4sin^3(2x) ?
The first derivative of 4sin^3(2x) is 24sin^2(2x)cos(2x)