What is the first d/(dt)(5sin(t)) ?

The first d/(dt)(5sin(t)) is 5cos(t)

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d/(dt)(5sin(t))

\frac{d}{d t} (5 sin (t))

5 cos (t)

Solution steps

\frac{d}{d t} (5 sin (t))

Take the constant out:

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

= 5 \frac{d}{d t} (sin (t))

Apply the common derivative:

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

= 5 cos (t)

2 (sin (2 t)) e^{- 2 t}

\frac{d}{d x} (x ln (\frac{x}{4}))

\frac{2}{s ^{2}}

x \to 5 lim (10)

\int sin^{7} (x co) s^{4} x d x