What is the d/(dθ)(2sin(5θ)) ?

The d/(dθ)(2sin(5θ)) is 10cos(5θ)

What is the first d/(dθ)(2sin(5θ)) ?

The first d/(dθ)(2sin(5θ)) is 10cos(5θ)

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\frac{d}{d θ} (2 sin (5 θ))

10 cos (5 θ)

Solution steps

\frac{d}{d θ} (2 sin (5 θ))

Take the constant out:

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

= 2 \frac{d}{d θ} (sin (5 θ))

Apply the chain rule:

cos (5 θ) \frac{d}{d θ} (5 θ)

= cos (5 θ) \frac{d}{d θ} (5 θ)

\frac{d}{d θ} (5 θ) = 5

= 2 cos (5 θ) \cdot 5

Simplify

= 10 cos (5 θ)

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