What is the d/(dθ)(2sin^2(θ)) ?

The d/(dθ)(2sin^2(θ)) is 2sin(2θ)

What is the first d/(dθ)(2sin^2(θ)) ?

The first d/(dθ)(2sin^2(θ)) is 2sin(2θ)

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\frac{d}{d θ} (2 sin^{2} (θ))

2 sin (2 θ)

Solution steps

\frac{d}{d θ} (2 sin^{2} (θ))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \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 \cdot 2 sin (θ) cos (θ)

Simplify

2 \cdot 2 sin (θ) cos (θ) : 2 sin (2 θ)

= 2 sin (2 θ)