What is the derivative of y=(sin(2x^3-1))^2 ?

The derivative of y=(sin(2x^3-1))^2 is 12x^2sin(2x^3-1)cos(2x^3-1)

What is the first derivative of y=(sin(2x^3-1))^2 ?

The first derivative of y=(sin(2x^3-1))^2 is 12x^2sin(2x^3-1)cos(2x^3-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = (sin (2 x^{3} - 1))^{2}

12 x^{2} sin (2 x^{3} - 1) cos (2 x^{3} - 1)

Solution steps

\frac{d}{d x} ((sin (2 x^{3} - 1))^{2})

Apply the chain rule:

2 sin (2 x^{3} - 1) \frac{d}{d x} (sin (2 x^{3} - 1))

= 2 sin (2 x^{3} - 1) \frac{d}{d x} (sin (2 x^{3} - 1))

\frac{d}{d x} (sin (2 x^{3} - 1)) = cos (2 x^{3} - 1) \cdot 6 x^{2}

= 2 sin (2 x^{3} - 1) cos (2 x^{3} - 1) \cdot 6 x^{2}

Simplify

= 12 x^{2} sin (2 x^{3} - 1) cos (2 x^{3} - 1)

What is the derivative of y=(sin(2x^3-1))^2 ?
The derivative of y=(sin(2x^3-1))^2 is 12x^2sin(2x^3-1)cos(2x^3-1)
What is the first derivative of y=(sin(2x^3-1))^2 ?
The first derivative of y=(sin(2x^3-1))^2 is 12x^2sin(2x^3-1)cos(2x^3-1)