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

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

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

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

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

4 cos (2 t)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

cos (2 t) \frac{d}{d t} (2 t)

= cos (2 t) \frac{d}{d t} (2 t)

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

= 2 cos (2 t) \cdot 2

Simplify

= 4 cos (2 t)

\frac{3 x + 1}{x ^{2} + 1}

y^{^{'}} = x + y, y (0) = 1

3 (2 z e^{z} + e^{z} z^{2})

f (x) = (x - 4)^{2}

\frac{d}{d x} (ln (e^{15 x}))