What is the derivative of sin^2(θ) ?

The derivative of sin^2(θ) is sin(2θ)

What is the first derivative of sin^2(θ) ?

The first derivative of sin^2(θ) is sin(2θ)

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derivative of

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)

What is the derivative of sin^2(θ) ?
The derivative of sin^2(θ) is sin(2θ)
What is the first derivative of sin^2(θ) ?
The first derivative of sin^2(θ) is sin(2θ)