What is the d/(dt)(2sin(4t)) ?

The d/(dt)(2sin(4t)) is 8cos(4t)

What is the first d/(dt)(2sin(4t)) ?

The first d/(dt)(2sin(4t)) is 8cos(4t)

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\frac{d}{d t} (2 sin (4 t))

8 cos (4 t)

Solution steps

\frac{d}{d t} (2 sin (4 t))

Take the constant out:

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

= 2 \frac{d}{d t} (sin (4 t))

Apply the chain rule:

cos (4 t) \frac{d}{d t} (4 t)

= cos (4 t) \frac{d}{d t} (4 t)

\frac{d}{d t} (4 t) = 4

= 2 cos (4 t) \cdot 4

Simplify

= 8 cos (4 t)

\frac{d y}{d t} + 2 y = 1

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