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

The d/(dt)(3tcos(t)) is 3(cos(t)-tsin(t))

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

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

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

3 (cos (t) - t sin (t))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = cos (t)

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

\frac{d t}{d t} = 1

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

= 3 (1 \cdot cos (t) + (- sin (t)) t)

Simplify

= 3 (cos (t) - t sin (t))

What is the d/(dt)(3tcos(t)) ?
The d/(dt)(3tcos(t)) is 3(cos(t)-tsin(t))
What is the first d/(dt)(3tcos(t)) ?
The first d/(dt)(3tcos(t)) is 3(cos(t)-tsin(t))