What is (\partial)/(\partial θ)(sin^2(θ)) ?

The answer to (\partial)/(\partial θ)(sin^2(θ)) is sin(2θ)

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(\partial)/(\partial θ)(sin^2(θ))

\frac{\partial}{\partial θ} (sin^{2} (θ))

sin (2 θ)

Solution steps

\frac{\partial}{\partial θ} (sin^{2} (θ))

Apply the chain rule:

2 sin (θ) \frac{\partial}{\partial θ} (sin (θ))

= 2 sin (θ) \frac{\partial}{\partial θ} (sin (θ))

\frac{\partial}{\partial 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)

\frac{d}{d r} ((r - s + cos (r + s) + sin (r + s))^{2})

\frac{d x}{d t} = 3 x t

x \to 1 lim (3 x^{2} + 2 x)

\int_{\frac{π}{2}}^{π} 4 cot (\frac{x}{3}) d x

n = 0 \sum \infty \frac{n}{( 2 n + 1 ) !}

What is (\partial)/(\partial θ)(sin^2(θ)) ?
The answer to (\partial)/(\partial θ)(sin^2(θ)) is sin(2θ)