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

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

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d/(dt)(4sin(t))

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

4 cos (t)

Solution steps

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

Take the constant out:

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

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

Apply the common derivative:

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

= 4 cos (t)

y^{^{''}} + 11 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = 0

f (x) = - \frac{3}{2} x^{2}

\int_{- 1}^{0} t e^{- j^{2} π f t} d t

\frac{d}{d x} (6 x^{2} + 6 x - 36)

(x^{\frac{1}{2}})^{^{'}}