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Popular >

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)

Popular Examples

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

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

limit as x approaches 1-of x/(x^2+1)

x \to 1 - lim (\frac{x}{x ^{2} + 1})

sum from n=1 to infinity of (n+1)/(2^n)

n = 1 \sum \infty \frac{n + 1}{2 ^{n}}

integral from 0 to pi of 4sin^4(x)

\int_{0}^{π} 4 sin^{4} (x) d x

derivative of x^2(x+2^3)

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

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)