What is the first d/(dt)(bsin(t)) ?

The first d/(dt)(bsin(t)) is bcos(t)

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d/(dt)(bsin(t))

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

b cos (t)

Solution steps

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

Take the constant out:

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

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

Apply the common derivative:

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

= b cos (t)

\frac{d}{d x} (x^{2} + e^{x^{2}})

\int sin^{3} (x) cos^{10} (x) d x

\frac{d}{d x} (\frac{2}{5} x^{\frac{5}{2}})

\int (x^{3} - 2 x^{\frac{1}{2}} + 4)^{2} d x

\frac{d}{d x} (\frac{1}{y - 5 x ^{2}})