What is the d/(dt)(3cos(t)) ?

The d/(dt)(3cos(t)) is -3sin(t)

What is the first d/(dt)(3cos(t)) ?

The first d/(dt)(3cos(t)) is -3sin(t)

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\frac{d}{d t} (3 cos (t))

- 3 sin (t)

Solution steps

\frac{d}{d t} (3 cos (t))

Take the constant out:

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

= 3 \frac{d}{d t} (cos (t))

Apply the common derivative:

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

= 3 (- sin (t))

Simplify

= - 3 sin (t)

x \to 0 lim (3 ln (x))

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\frac{d}{d x} (\frac{x ^{2} + x - 6}{x ^{2} - 4 x + 3})