What is the d/(dt)(sin(ωt+θ)) ?

The d/(dt)(sin(ωt+θ)) is cos(ωt+θ)ω

What is the first d/(dt)(sin(ωt+θ)) ?

The first d/(dt)(sin(ωt+θ)) is cos(ωt+θ)ω

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\frac{d}{d t} (sin (ω t + θ))

cos (ω t + θ) ω

Solution steps

\frac{d}{d t} (sin (ω t + θ))

Treat

ω, θ

as a constant

Apply the chain rule:

cos (ω t + θ) \frac{d}{d t} (ω t + θ)

= cos (ω t + θ) \frac{d}{d t} (ω t + θ)

\frac{d}{d t} (ω t + θ) = ω

= cos (ω t + θ) ω