What is the derivative of sin^3(3x^2+6x) ?

The derivative of sin^3(3x^2+6x) is 3sin^2(3x^2+6x)cos(3x^2+6x)(6x+6)

What is the first derivative of sin^3(3x^2+6x) ?

The first derivative of sin^3(3x^2+6x) is 3sin^2(3x^2+6x)cos(3x^2+6x)(6x+6)

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\frac{d}{d x} (sin^{3} (3 x^{2} + 6 x))

3 sin^{2} (3 x^{2} + 6 x) cos (3 x^{2} + 6 x) (6 x + 6)

Solution steps

\frac{d}{d x} (sin^{3} (3 x^{2} + 6 x))

Apply the chain rule:

3 (sin (3 x^{2} + 6 x))^{2} \frac{d}{d x} (sin (3 x^{2} + 6 x))

= 3 (sin (3 x^{2} + 6 x))^{2} \frac{d}{d x} (sin (3 x^{2} + 6 x))

\frac{d}{d x} (sin (3 x^{2} + 6 x)) = cos (3 x^{2} + 6 x) (6 x + 6)

= 3 (sin (3 x^{2} + 6 x))^{2} cos (3 x^{2} + 6 x) (6 x + 6)

Simplify

= 3 sin^{2} (3 x^{2} + 6 x) cos (3 x^{2} + 6 x) (6 x + 6)

\int_{0}^{3} (\frac{x}{3} + 5) d x

\frac{d}{d x} (\frac{5 - x ^{2}}{5 + x ^{2}})

\frac{\partial}{\partial x} (\frac{1}{6} x^{3})

f (x) = 2 x^{2} + 3 x - 2, (- 1, - 3)

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

What is the derivative of sin^3(3x^2+6x) ?
The derivative of sin^3(3x^2+6x) is 3sin^2(3x^2+6x)cos(3x^2+6x)(6x+6)
What is the first derivative of sin^3(3x^2+6x) ?
The first derivative of sin^3(3x^2+6x) is 3sin^2(3x^2+6x)cos(3x^2+6x)(6x+6)