What is the d/(dθ)(sin^2(θ)) ?

The d/(dθ)(sin^2(θ)) is sin(2θ)

What is the first d/(dθ)(sin^2(θ)) ?

The first d/(dθ)(sin^2(θ)) is sin(2θ)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d θ} (sin^{2} (θ))

sin (2 θ)

Solution steps

\frac{d}{d θ} (sin^{2} (θ))

Apply the chain rule:

2 sin (θ) \frac{d}{d θ} (sin (θ))

= 2 sin (θ) \frac{d}{d θ} (sin (θ))

\frac{d}{d θ} (sin (θ)) = cos (θ)

= 2 sin (θ) cos (θ)

Use the Double Angle identity:

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

= sin (2 θ)