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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

\int_{0}^{3} t e^{- t} d t

\int 6 x^{2} - 5 x + 3 d x

\int (6 sin (2 x) - 4 cos (4 x)) d x

y^{2} = 4 x, 4 x - 3 y = 4

(arctan (9 x))^{2}

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