What is the d/(dt)(scos(t)) ?

The d/(dt)(scos(t)) is -ssin(t)

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

The first d/(dt)(scos(t)) is -ssin(t)

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

- s sin (t)

Solution steps

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

Take the constant out:

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

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

Apply the common derivative:

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

= s (- sin (t))

Simplify

= - s sin (t)

\frac{d y}{d x}, x^{y} = y^{x}

x \to 2 lim ((x - 2)^{2})

y = cos^{3} (4 x^{6} + 10)

x^{2} - 7 x + 12

\int \frac{2 x ^{2} - x - 20}{x ^{2} + x - 6} d x