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)

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\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)

y^{^{''}} + 49 y = 3 tan (7 x)

f (x) = 2 x + 7, at x = 9

y^{^{'}} + 0.7 y - 18.2 = 0

\int \frac{4 x - 11}{x ^{2} - 3 x - 4} d x

\frac{d}{d x} (e^{x} cos (3 x))