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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

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

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