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

The derivative of (sin(3x)^3) is 9sin^2(3x)cos(3x)

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

The first derivative of (sin(3x)^3) is 9sin^2(3x)cos(3x)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= 9 sin^{2} (3 x) cos (3 x)

x \to 0 lim ((1 - \frac{1}{x}) x)

\frac{\partial}{\partial x} (- 5 x cos (x^{2} - 5 x y))

\frac{d ^{2}}{d x} (y) + 2 \frac{d y}{d x} + y = 0

\frac{\partial}{\partial x} (e^{- 2 z} y sin (x))

cos (θ), 0.5

What is the derivative of (sin(3x)^3) ?
The derivative of (sin(3x)^3) is 9sin^2(3x)cos(3x)
What is the first derivative of (sin(3x)^3) ?
The first derivative of (sin(3x)^3) is 9sin^2(3x)cos(3x)